"""
Write a python function to find the index of smallest triangular number with n digits.
assert find_Index(2) == 4
"""
import math
def find_Index(n):
x = math.sqrt(2 * math.pow(10,(n - 1)))
return round(x)
[[2], [3], [4]]
[[5], [1], [100], [2], [4], [6], [99], [101], [True], [3], [98], [7], [8], [9], [10], [57], [12], [11], [13], [91], [102], [14], [90], [56], [54], [97], [55], [53], [103], [52], [94], [92], [104], [58], [15], [95], [16], [51], [93], [59], [17], [96], [83], [82], [89], [18], [60], [84], [19], [62], [50], [42], [61], [49], [48], [88], [81], [106], [41], [40], [105], [85], [20], [21], [67], [68], [80], [69], [29], [86], [22], [25], [39], [47], [63], [46], [30], [28], [26], [23], [43], [64], [87], [38], [65], [44], [27], [79], [66], [31], [107], [45], [108], [70], [24], [109], [78], [33], [77], [110], [111], [32], [71]]
code-llama-multi-7b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
"""
Find the index of smallest triangular number with n digits.
:param n: number of digits
:return: index of smallest triangular number with n digits
"""
if n == 1:
return 1
if n == 2:
return 3
if n == 3:
return 6
if n == 4:
return 10
if n == 5:
return 15
if n == 6:
return 21
if n == 7:
return 28
if n == 8:
return 36
if n == 9:
return 45
if n == 10:
return 55
if n == 11:
return 66
if n == 12:
return 78
if n == 13:
return 91
if n == 14:
return 105
if n == 15:
return 120
if n == 16:
return 136
if n == 17:
return 153
if n == 18:
return 171
if n == 19:
return 189
if n == 20:
return 209
if n == 21:
return 229
if n == 22:
return 249
if n == 23:
return 269
if n == 24:
return 291
if n == 25:
return 315
if n == 26:
return 341
if n == 27:
return 368
if n == 28:
return 396
if n == 29:
return 425
if n == 30:
return 456
if n ==
databricks--dbrx-instruct. fail_base: True, fail_plus: True
def find_index(n):
"""
Find the index of the smallest triangular number with n digits.
:param n: int - number of digits
:return: int - index of the smallest triangular number with n digits
"""
if n < 1 or type(n) != int:
raise ValueError("Input must be a positive integer")
triangular_numbers = []
i = 0
while True:
triangular_number = sum(range(i + 1))
if len(str(triangular_number)) == n:
triangular_numbers.append(triangular_number)
break
elif len(str(triangular_number)) > n:
break
i += 1
return triangular_numbers[0]
# Test the function
assert find_index(2) == 4
CohereForAI--c4ai-command-r-plus. fail_base: True, fail_plus: True
def find_Index(n):
def is_triangular(num):
return num * (num + 1) // 2
num = 10 ** (n - 1) - 1
while True:
if is_triangular(num):
return num
num += 1
```
claude-3-haiku-20240307. fail_base: False, fail_plus: True
Here's the solution wrapped in a Python markdown block:
```python
def find_Index(n):
"""
Find the index of the smallest triangular number with n digits.
Args:
n (int): The number of digits.
Returns:
int: The index of the smallest triangular number with n digits.
"""
i = 1
while True:
triangular_num = (i * (i + 1)) // 2
if len(str(triangular_num)) == n:
return i
elif len(str(triangular_num)) > n:
return i - 1
i += 1
code-millenials-34b. fail_base: False, fail_plus: True
def find_Index(n):
# Initialize result
result = 0
# Find first triangular number with n digits
while True:
result += 1
if len(str(result*(result+1)//2)) == n:
return result
# Test the function
assert find_Index(2) == 4
dolphin-2.6. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# Calculate the smallest triangular number with n digits
triangular_numbers = []
num = 1
while len(str(num)) < n:
triangular_numbers.append(num)
num += 1
smallest_triangular_number = min(triangular_numbers)
# Calculate the index of the smallest triangular number
index = 0
for i in range(len(triangular_numbers)):
if triangular_numbers[i] == smallest_triangular_number:
index = i
break
return index
# Test the function
assert find_Index(2) == 4
claude-3-opus-20240229. fail_base: False, fail_plus: True
Here's the Python code to find the index of the smallest triangular number with n digits, wrapped in a Python markdown block:
```python
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# Initialize variables
index = 1
triangular_num = 1
# Iterate until the triangular number has n digits
while len(str(triangular_num)) < n:
index += 1
triangular_num += index
return index
# Test the function
assert find_Index(2) == 4
mixtral-8x7b-instruct. fail_base: True, fail_plus: True
def is_n_digit(n, triangular_number):
"""Return True if triangular number has n digits, else False"""
return len(str(triangular_number)) == n
wizardcoder-34b. fail_base: False, fail_plus: True
Here's the Python function to find the index of the smallest triangular number with n digits:
```python
def find_Index(n):
"""
This function finds the index of the smallest triangular number with n digits.
"""
# Initialize variables
count = 0
i = 1
# Loop until the number of digits of triangular number is n
while True:
count += 1
triangular_num = (count * (count + 1)) // 2
# Check if the number of digits of triangular number is n
if len(str(triangular_num)) == n:
return count
# If the number of digits of triangular number is greater than n, return the previous index
elif len(str(triangular_num)) > n:
return count - 1
# Increment the count
i += 1
```
We can test the function with the given assertion:
```python
assert find_Index(2) == 4
```
This will return True since the smallest triangular number with 2 digits is 3 (1 + 2 = 3) and its index is 4.
mixtral-8x22b-instruct-v0.1. fail_base: True, fail_plus: True
def find_index(n):
"""
Find the index of the smallest triangular number with n digits.
A triangular number is a number that is the sum of the first n natural numbers.
For example, the first few triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
The index of a triangular number is its position in the sequence of triangular numbers.
For example, the index of the triangular number 10 is 4, because it is the 4th triangular number.
The function find_index(n) returns the index of the smallest triangular number with n digits.
For example, find_index(2) returns 4, because the smallest triangular number with 2 digits is 10,
and its index is 4.
The function uses a binary search algorithm to find the index of the smallest triangular number with n digits.
The binary search algorithm works by repeatedly dividing the search interval in half.
If the value of the triangular number at the midpoint of the interval is less than 10^(n-1),
then the index of the smallest triangular number with n digits is in the right half of the interval.
Otherwise, it is in the left half of the interval.
The binary search algorithm continues until the search interval is empty.
The function find_index(n) returns the index of the smallest triangular number with n digits.
"""
# Initialize the search interval
left = 1
right = 10**n
# Binary search algorithm
while left < right:
mid = (left + right) // 2
triangular_number = mid * (mid + 1) // 2
if triangular_number < 10**(n-1):
left = mid + 1
else:
right = mid
# Return the index of the smallest triangular number with n digits
return left
# Test the function
assert find_index(2) == 4
code-llama-multi-34b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return find_Index(n-1) + 9 * (10 ** (n-1))
if __name__ == "__main__":
assert find_Index(2) == 4
Qwen--Qwen1.5-72B-Chat. fail_base: True, fail_plus: True
def is_triangular(n):
i = 1
triangular_number = 1
while triangular_number < n:
i += 1
triangular_number += i
return triangular_number == n
def find_Index(n):
i = 1
index = 1
while True:
if is_triangular(index):
i += 1
if i == n:
return index
index += 1
# Test cases
assert find_Index(2) == 4
assert find_Index(3) == 10
assert find_Index(4) == 49
mistral-large-latest. fail_base: False, fail_plus: True
Sure, here is the Python code to solve the problem:
```python
import math
def find_Index(n):
# Initialize result
res = 0
# Run a loop until number of digits
# in res become n
while(True):
# Update res
res += 1
# Check if number of digits
# in res are n or not
if (math.floor(math.log10(res * (res + 1) * 0.5)) + 1 == n):
break
return res
# Test the function
assert find_Index(2) == 4
```
This function uses a while loop to keep incrementing the index until the triangular number at that index has the required number of digits. The logarithm function is used to count the number of digits in the triangular number.
codegen-2b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return n*(n+1)//2
print(find_Index(2))
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return n*(n+1)//2
print(find_Index(2))
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return n*(n+1)//2
print(find_Index(2))
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return n*(n+1)//2
print(find_Index(2))
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return n*(n+1)//2
print(find_Index(2))
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-
HuggingFaceH4--starchat2-15b-v0.1. fail_base: False, fail_plus: True
def find_Index(n):
"""
Write a python function to find the index of smallest triangular number with n digits.
assert find_Index(2) == 4
"""
index = 1
while True:
triangular_number = index * (index + 1) // 2
if len(str(triangular_number)) == n:
return index
index += 1
# Test the function
assert find_Index(2) == 4
codegemma-7b. fail_base: False, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
i = 1
while True:
if len(str(i * (i + 1) // 2)) == n:
return i
i += 1
code-llama-multi-13b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
"""
:param n: number of digits
:return: index of smallest triangular number with n digits
"""
if n == 1:
return 1
elif n == 2:
return 4
elif n == 3:
return 10
elif n == 4:
return 20
elif n == 5:
return 35
elif n == 6:
return 56
elif n == 7:
return 84
elif n == 8:
return 120
elif n == 9:
return 165
elif n == 10:
return 220
elif n == 11:
return 286
elif n == 12:
return 364
elif n == 13:
return 455
elif n == 14:
return 560
elif n == 15:
return 680
elif n == 16:
return 816
elif n == 17:
return 965
elif n == 18:
return 1130
elif n == 19:
return 1315
elif n == 20:
return 1525
elif n == 21:
return 1750
elif n == 22:
return 1995
elif n == 23:
return 2256
elif n == 24:
return 2530
elif n == 25:
return 2825
elif n == 26:
return 3140
elif n == 27:
return 3470
elif n == 28:
return 3820
elif n == 29:
return 4200
elif n == 30:
return 461
deepseek-coder-6.7b-instruct. fail_base: False, fail_plus: True
Here is the Python function in a markdown style code block:
```python
def find_Index(n):
"""
This function finds the index of the smallest triangular number with n digits.
The formula used here is:
index = ceil((sqrt((8 * 10^(n-1)) + 1) - 1) / 2)
"""
import math
return math.ceil((math.sqrt((8 * (10 ** (n - 1))) + 1) - 1) / 2)
# Test the function
assert find_Index(2) == 4
```
This function uses the formula given in the link you provided to calculate the index of the smallest triangular number with n digits. The `math.ceil()` function is used to round up the result to the nearest integer. The function is tested with `n=2`, and the result is asserted to be `4`.
open-hermes-2.5-code-290k-13b. fail_base: True, fail_plus: True
def find_Index(n):
# Calculate the upper limit of the triangular number
upper_limit = 10 ** (n - 1)
# Iterate through the range of possible triangular numbers
for i in range(1, upper_limit + 1):
# Calculate the number of digits in the current triangular number
num_digits = len(str(i))
# If the number of digits matches the desired value, return the index
if num_digits == n:
return i
# If no triangular number with the desired number of digits is found, return -1
return -1
# Test the function with n = 2
assert find_Index(2) == 4
codet5p-6b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
i = 1
while True:
i += 1
n_digits = i * (i + 1) // 2
if n_digits == n:
return i
elif n_digits > n:
return i - 1
print(find_Index(2))
print(find_Index(3))
print(find_Index(4))
print(find_Index(5))
print(find_Index(6))
print(find_Index(7))
print(find_Index(8))
print(find_Index(9))
print(find_Index(10))
print(find_Index(11))
print(find_Index(12))
print(find_Index(13))
print(find_Index(14))
print(find_Index(15))
print(find_Index(16))
print(find_Index(17))
print(find_Index(18))
print(find_Index(19))
print(find_Index(20))
print(find_Index(21))
print(find_Index(22))
print(find_Index(23))
print(find_Index(24))
print(find_Index(25))
print(find_Index(26))
print(find_Index(27))
print(find_Index(28))
print(find_Index(29))
print(find_Index(30))
print(find_Index(31))
print(find_Index(32))
print(find_Index(33))
print(find_Index(34))
print(find_Index(35))
print(find_Index(36))
print(find_Index(37))
print(find_Index(38))
print(find_Index(39))
print(find_Index(40))
print(find_Index(41))
print(find_Index(42))
print(find_Index(43))
print(find_Index(44))
print(find_Index(45))
print(find_Index(46))
print(find_Index(47))
print(find_Index(48))
print(find_Index(49))
print(find_Index(50))
codegemma-7b-it. fail_base: False, fail_plus: True
def find_Index(n):
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
i = 1
sum = 0
while True:
sum += i
if len(str(sum)) == n:
return i
i += 1
mistralai--Mistral-7B-Instruct-v0.2. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits.
assert find_Index(2) == 4
"""
def triangular_number(n):
return int((n * (n + 1) / 2))
def find_index(n):
current = 0
index = 0
while len(str(triangular_number(index))) < n:
current += 1
index += 1
return current
xwincoder-34b. fail_base: True, fail_plus: True
def find_index(n):
triangular_numbers = [0]
index = 1
while len(str(triangular_numbers[-1])) < n:
triangular_numbers.append(triangular_numbers[-1] + index)
index += 1
return index - 1
# Test the function
assert find_index(2) == 4
wizardcoder-15b. fail_base: True, fail_plus: True
Here's the Python function to find the index of smallest triangular number with n digits:
```python
def find_Index(n):
# Initialize the variable to store the smallest triangular number with n digits
smallest_triangular = 10**(n-1)
# Initialize the variable to store the index of the smallest triangular number with n digits
index = n-1
# Loop through all the triangular numbers with n digits and find the smallest one
for i in range(n-1, 10**n):
triangular = i*(i+1)//2
# If the current triangular number is smaller than the smallest triangular number with n digits, update the variables
if triangular < smallest_triangular:
smallest_triangular = triangular
index = i
return index
```
The function takes an integer `n` as input and returns the index of the smallest triangular number with `n` digits. The function first initializes the variable `smallest_triangular` to the smallest triangular number with `n-1` digits (since the smallest triangular number with `n` digits is the smallest triangular number with `n-1` digits plus 1). It then initializes the variable `index` to `n-1`, since the index of the smallest triangular number with `n` digits is `n-1`.
The function then loops through all the triangular numbers with `n` digits (from `n-1` to `10**n-1`) and finds the smallest one. For each triangular number, it calculates the corresponding index `i` and checks if it is smaller than the current smallest triangular number with `n` digits. If it is, it updates the variables `smallest_triangular` and `index` accordingly.
Finally, the function returns the index of the smallest triangular number with `n` digits.
To test the function, we can use the `assert` statement:
```python
assert find_Index(2) == 4
```
This asserts that the function returns `4` for `n=2`, which is the index of the smallest triangular number with `2` digits (which is `4`).
code-llama-34b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return find_Index(n-1) + 9 * 10 ** (n-2) + n
deepseek-coder-33b-instruct. fail_base: True, fail_plus: True
Here is the Python function to find the index of smallest triangular number with n digits:
```python
def find_Index(n):
if n == 1:
return 1
left, right = 1, n * 10
while left < right:
mid = (left + right) // 2
if mid * (mid + 1) // 2 >= 10 ** (n - 1):
right = mid
else:
left = mid + 1
return left
# Test the function
print(find_Index(2)) # Output: 4
```
This function uses binary search to find the smallest index that makes the triangular number have n digits. The triangular number is calculated by the formula `n * (n + 1) / 2`. The binary search is performed on the index, and the mid-point is checked to see if it produces a triangular number with n digits. If it does, the right boundary is moved to the mid-point, otherwise, the left boundary is moved to the mid-point plus one. The binary search continues until the left boundary equals the right boundary, which is the smallest index that makes the triangular number have n digits.
phi-2. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
"""
Find the index of smallest triangular number with n digits.
"""
# Initialize the triangular number
triangular_number = 1
# Initialize the index
index = 1
# Loop until the triangular number has n digits
while len(str(triangular_number)) < n:
# Increment the triangular number
triangular_number += index
# Increment the index
index += 1
# Return the index
return index
# Test the function
assert find_Index(2) == 4
assert find_Index(3) == 10
assert find_Index(4) == 15
assert find_Index(5) == 21
assert find_Index(6) == 28
assert find_Index(7) == 36
assert find_Index(8) == 45
assert find_Index(9) == 55
assert find_Index(10) == 66
assert find_Index(11) == 78
assert find_Index(12) == 91
assert find_Index(13) == 105
assert find_Index(14) == 120
assert find_Index(15) == 136
assert find_Index(16) == 153
assert find_Index(17) == 171
assert find_Index(18) == 189
assert find_Index(19) == 201
assert find_Index(20) == 210
assert find_Index(21) == 231
assert find_Index(22) == 252
assert find_Index(23) == 273
assert find_Index(24) == 285
assert find_Index(25) == 301
assert find_Index(26) == 315
assert find_Index(27) == 336
assert find_Index(28) == 351
assert find_Index(29) == 378
assert find_Index(30) == 405
assert find_Index(31) == 420
assert find_Index(32) == 441
assert find_Index(33) == 462
assert find_Index(34) == 483
assert find_Index(35) == 504
assert find_Index(36) == 528
assert find_Index(37) == 561
assert find_Index(38) == 594
assert find_Index(39) == 615
codet5p-2b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
return (n*(n+1))//2
print(find_Index(2))
print(find_Index(3))
print(find_Index(4))
print(find_Index(5))
print(find_Index(6))
print(find_Index(7))
print(find_Index(8))
print(find_Index(9))
print(find_Index(10))
print(find_Index(11))
print(find_Index(12))
print(find_Index(13))
print(find_Index(14))
print(find_Index(15))
print(find_Index(16))
print(find_Index(17))
print(find_Index(18))
print(find_Index(19))
print(find_Index(20))
print(find_Index(21))
print(find_Index(22))
print(find_Index(23))
print(find_Index(24))
print(find_Index(25))
print(find_Index(26))
print(find_Index(27))
print(find_Index(28))
print(find_Index(29))
print(find_Index(30))
print(find_Index(31))
print(find_Index(32))
print(find_Index(33))
print(find_Index(34))
print(find_Index(35))
print(find_Index(36))
print(find_Index(37))
print(find_Index(38))
print(find_Index(39))
print(find_Index(40))
print(find_Index(41))
print(find_Index(42))
print(find_Index(43))
print(find_Index(44))
print(find_Index(45))
print(find_Index(46))
print(find_Index(47))
print(find_Index(48))
print(find_Index(49))
print(find_Index(50))
print(find_Index(51))
print(find_Index(52))
print(find_Index(53))
print(find_Index(54))
print(find_Index(55))
print(find
bigcode--starcoder2-15b-instruct-v0.1. fail_base: True, fail_plus: True
def find_index(n):
"""
Find the index of the smallest triangular number with n digits.
"""
index = 1
while True:
triangular_number = index * (index + 1) // 2
if len(str(triangular_number)) == n:
return index
index += 1
codegemma-2b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
for i in range(1, n+1):
if i*(i+1)/2 == n:
return i
return -1
<|file_separator|>
white-rabbit-neo-33b-v1. fail_base: False, fail_plus: True
def find_Index(n):
# Initialize the index and the current triangular number
index = 1
triangular_number = 1
# Loop until we find a triangular number with n digits
while True:
# Calculate the next triangular number
index += 1
triangular_number += index
# Convert the triangular number to a string and check its length
if len(str(triangular_number)) == n:
return index
# Test the function
assert find_Index(2) == 4
microsoft--Phi-3-mini-4k-instruct. fail_base: True, fail_plus: True
def find_index(n):
"""
Find the index of the smallest triangular number with n digits.
:param n: Number of digits
:return: Index of the smallest triangular number with n digits
"""
# Start from the first triangular number
index = 1
while True:
# Calculate the current triangular number
triangular_number = (index * (index + 1)) // 2
# Check if the number of digits is equal to n
if len(str(triangular_number)) == n:
return index
# Increment the index
index += 1
# Test the function
assert find_index(2) == 4
assert find_index(3) == 12
assert find_index(4) == 21
speechless-codellama-34b. fail_base: True, fail_plus: True
def find_Index(n):
# Initialize the lower and upper bounds
low = 1
high = 10 ** n
# Calculate the middle index
mid = (low + high) // 2
# Calculate the triangular number at the middle index
triangular_number = mid * (mid + 1) // 2
# Check if the triangular number has n digits
while len(str(triangular_number)) != n:
# If the triangular number has more than n digits,
# update the lower bound to the middle index
if len(str(triangular_number)) > n:
low = mid
# If the triangular number has less than n digits,
# update the upper bound to the middle index
else:
high = mid
# Calculate the middle index
mid = (low + high) // 2
# Calculate the triangular number at the middle index
triangular_number = mid * (mid + 1) // 2
# Return the index of the smallest triangular number with n digits
return mid
# Test the function
assert find_Index(2) == 4
```
meta-llama-3-70b-instruct. fail_base: False, fail_plus: True
def find_Index(n):
count = 1
triangular_num = 1
while True:
digits = len(str(triangular_num))
if digits == n:
return count
count += 1
triangular_num += count
assert find_Index(2) == 4
stable-code-3b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
return int(n*(n+1)/2)
print(find_Index(2))
print(find_Index(3))
print(find_Index(4))
print(find_Index(5))
print(find_Index(6))
print(find_Index(7))
print(find_Index(8))
print(find_Index(9))
print(find_Index(10))
print(find_Index(11))
print(find_Index(12))
print(find_Index(13))
print(find_Index(14))
print(find_Index(15))
print(find_Index(16))
print(find_Index(17))
print(find_Index(18))
print(find_Index(19))
print(find_Index(20))
print(find_Index(21))
print(find_Index(22))
print(find_Index(23))
print(find_Index(24))
print(find_Index(25))
print(find_Index(26))
print(find_Index(27))
print(find_Index(28))
print(find_Index(29))
print(find_Index(30))
print(find_Index(31))
print(find_Index(32))
print(find_Index(33))
print(find_Index(34))
print(find_Index(35))
print(find_Index(36))
print(find_Index(37))
print(find_Index(38))
print(find_Index(39))
print(find_Index(40))
print(find_Index(41))
print(find_Index(42))
print(find_Index(43))
print(find_Index(44))
print(find_Index(45))
print(find_Index(46))
print(find_Index(47))
print(find_Index(48))
print(find_Index(49))
print(find_Index(50))
print(find_Index(51))
print(find_Index(52))
print(find_Index(53))
print(find_Index(54))
print(find_Index(55))
print(find
codegen-6b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
"""
:param n: number of digits
:return: index of smallest triangular number with n digits
"""
if n == 1:
return 1
if n == 2:
return 3
if n == 3:
return 6
if n == 4:
return 10
if n == 5:
return 15
if n == 6:
return 21
if n == 7:
return 28
if n == 8:
return 36
if n == 9:
return 45
if n == 10:
return 55
if n == 11:
return 66
if n == 12:
return 77
if n == 13:
return 89
if n == 14:
return 101
if n == 15:
return 113
if n == 16:
return 126
if n == 17:
return 139
if n == 18:
return 152
if n == 19:
return 165
if n == 20:
return 176
if n == 21:
return 187
if n == 22:
return 199
if n == 23:
return 212
if n == 24:
return 225
if n == 25:
return 236
if n == 26:
return 249
if n == 27:
return 262
if n == 28:
return 275
if n == 29:
return 288
if n == 30:
return 301
if n == 31:
return 314
if n == 32:
return 327
if n == 33:
return 340
if n == 34:
return 354
if n == 35:
return 367
if n == 36:
return 380
if n == 37:
return 393
if n == 38:
return 406
if n == 39:
return 419
if n == 40:
return 432
if n == 41:
return 445
if n == 42:
return 468
if n == 43:
return 481
gpt-4-1106-preview. fail_base: False, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
import math
def find_Index(n):
# Function to find the index of smallest triangular number
# with n digits
# A Triangular number or a triangle number counts objects arranged in an equilateral triangle. Triangular numbers are therefore
# given by the formula: Tn = n * (n + 1) / 2
# The idea is to use binary search on the result. First find the upper
# limit of result, then apply binary search
# Find the upper limit
low = 1
high = 10
while len(str((high * (high + 1)) // 2)) < n:
low = high
high *= 10
# Apply binary search
while low < high:
mid = (low + high) // 2
num = (mid * (mid + 1)) // 2
if len(str(num)) == n:
high = mid
elif len(str(num)) < n:
low = mid + 1
else:
high = mid - 1
# Since we are finding the smallest index, we need to move back to find
# the first occurrence of the number with n digits
while len(str(((high - 1) * high) // 2)) == n:
high -= 1
return high
# Example usage
# assert find_Index(2) == 4
gemma-7b-it. fail_base: True, fail_plus: True
def find_Index(n):
"""
Write a python function to find the index of smallest triangular number with n digits.
Args:
n: The number of digits in the smallest triangular number.
Returns:
The index of the smallest triangular number with n digits.
"""
# Calculate the triangular number with n digits.
triangular_number = n * (n + 1) // 2
# Find the index of the smallest triangular number with n digits.
index = 1
while triangular_number % 10 ** index != 0:
index += 1
# Return the index of the smallest triangular number with n digits.
return index
assert find_Index(2) == 4
opencodeinterpreter-ds-33b. fail_base: False, fail_plus: True
```python
def find_Index(n):
# The formula to find the index of smallest triangular number with n digits is (n*(n+1))/2
# We need to find the smallest n such that (n*(n+1))/2 >= 10^(n-1)
# We can use binary search to find the smallest n
left, right = 1, 10**6
while left < right:
mid = (left + right) // 2
if mid * (mid + 1) // 2 >= 10**(n-1):
right = mid
else:
left = mid + 1
return left
# Test the function
print(find_Index(2)) # Output: 4
openchat. fail_base: True, fail_plus: True
def find_Index(n):
# A triangular number is a number that can be obtained by summing consecutive integers.
# The nth triangular number is given by the formula n*(n+1)/2
# We need to find the smallest triangular number with n digits
# The smallest triangular number with n digits will have n+1 digits (since it will be n*(n+1)/2)
# So, we need to find the smallest triangular number with n+1 digits
# The smallest triangular number with n+1 digits is (n+1)*(n+2)/2
# We can start from 1 and keep increasing n until we find a triangular number with n+1 digits
# We can use a while loop to do this
i = 1
while True:
triangular_number = i*(i+1)//2
if len(str(triangular_number)) == n+1:
return i
i += 1
# Test the function
assert find_Index(2) == 4
speechless-starcoder2-7b. fail_base: False, fail_plus: True
def find_Index(n):
# Initialize the index
index = 0
# Loop until we find a triangular number with n digits
while True:
# Calculate the triangular number
triangular_number = (index * (index + 1)) // 2
# If the number of digits is equal to n, return the index
if len(str(triangular_number)) == n:
return index
# Increment the index
index += 1
# Test the function
assert find_Index(2) == 4
wizardcoder-7b. fail_base: False, fail_plus: True
Here's a Python function that finds the index of the smallest triangular number with n digits:
```python
def find_Index(n):
i = 1
while True:
triangular_number = i * (i + 1) // 2
if len(str(triangular_number)) == n:
return i
i += 1
```
This function uses a while loop to generate triangular numbers one by one and checks if the length of the triangular number is equal to n. If it is, it returns the value of i, which is the index of the smallest triangular number with n digits. The loop continues until a triangular number with n digits is found. The formula for generating triangular numbers is `i * (i + 1) // 2`. We use integer division `//` to ensure that the result is an integer.
octocoder. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 1
else:
return (n * (n + 1)) // 2
gemma-1.1-7b-it. fail_base: True, fail_plus: True
def find_Index(n):
i = 1
while str(i**3).count('0') > n:
i += 1
return i-1
"""
assert find_Index(2) == 4
"""
deepseek-coder-6.7b-base. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# Initialize result
res = 0
# One by one compute sum of
# digits in count of numbers
# from 1 to n.
for i in range(1, n + 1):
res = res + n // i
return res
# Driver code
n = 2
print(find_Index(n))
codegen-16b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# n = int(input())
# n = 2
# n = 3
# n = 4
# n = 5
# n = 6
# n = 7
# n = 8
# n = 9
# n = 10
# n = 11
# n = 12
# n = 13
# n = 14
# n = 15
# n = 16
# n = 17
# n = 18
# n = 19
# n = 20
# n = 21
# n = 22
# n = 23
# n = 24
# n = 25
# n = 26
# n = 27
# n = 28
# n = 29
# n = 30
# n = 31
# n = 32
# n = 33
# n = 34
# n = 35
# n = 36
# n = 37
# n = 38
# n = 39
# n = 40
# n = 41
# n = 42
# n = 43
# n = 44
# n = 45
# n = 46
# n = 47
# n = 48
# n = 49
# n = 50
# n = 51
# n = 52
# n = 53
# n = 54
# n = 55
# n = 56
# n = 57
# n = 58
# n = 59
# n = 60
# n = 61
# n = 62
# n = 63
# n = 64
# n = 65
# n = 66
# n = 67
# n = 68
# n = 69
# n = 70
# n = 71
# n = 72
# n = 73
# n = 74
# n = 75
# n = 76
# n = 77
# n = 78
# n = 79
# n = 80
# n = 81
# n = 82
# n = 83
#
mistral-7b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
"""
:param n: number of digits
:return: index of smallest triangular number with n digits
"""
if n == 1:
return 1
else:
return n + find_Index(n - 1)
assert find_Index(2) == 4
speechless-mistral-7b. fail_base: True, fail_plus: True
def find_Index(n):
triangular_numbers = []
for i in range(1, 10**n):
triangular_numbers.append(i*(i+1)//2)
return triangular_numbers.index(min(triangular_numbers)) + 1
assert find_Index(2) == 4
```
This Python script defines a function `find_Index` that takes an integer `n` as input and returns the index of the smallest triangular number with `n` digits. The function first generates a list of triangular numbers up to `10**n` using a loop, then finds the index of the smallest number in the list using the `index` method of the list, and finally adds 1 to the index to account for the fact that Python uses zero-based indexing. The assert statement at the end checks that the function correctly returns 4 for the input 2, as per the problem statement.
codet5p-16b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
i = 1
while True:
if len(str(i)) == n:
return i
i += 1
assert find_Index(2) == 4
assert find_Index(3) == 6
assert find_Index(4) == 8
assert find_Index(5) == 10
assert find_Index(6) == 12
assert find_Index(7) == 14
assert find_Index(8) == 16
assert find_Index(9) == 18
assert find_Index(10) == 20
assert find_Index(11) == 22
assert find_Index(12) == 24
assert find_Index(13) == 26
assert find_Index(14) == 28
assert find_Index(15) == 30
assert find_Index(16) == 32
assert find_Index(17) == 34
assert find_Index(18) == 36
assert find_Index(19) == 38
assert find_Index(20) == 40
assert find_Index(21) == 42
assert find_Index(22) == 44
assert find_Index(23) == 46
assert find_Index(24) == 48
assert find_Index(25) == 50
assert find_Index(26) == 52
assert find_Index(27) == 54
assert find_Index(28) == 56
assert find_Index(29) == 58
assert find_Index(30) == 60
assert find_Index(31) == 62
assert find_Index(32) == 64
assert find_Index(33) == 66
assert find_Index(34) == 68
assert find_Index(35) == 70
assert find_Index(36) == 72
assert find_Index(37) == 74
assert find_Index(38) == 76
assert find_Index(39) == 78
assert find_Index(40) == 80
assert find_Index(41) == 82
assert find_Index(42) == 84
assert find_Index(43) == 86
assert find_Index(44) == 88
assert find_Index(45) == 90
assert find_Index(46) == 92
assert find_Index(47) == 94
assert find_Index(48) == 96
assert
code-llama-13b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
index = 0
for i in range(1, n + 1):
index += i
return index
if __name__ == "__main__":
print(find_Index(2))
xdan-l1-chat. fail_base: True, fail_plus: True
def find_Index(n):
# Initialize the smallest triangular number with n digits
smallest_triangular_number = 10**(n-1)
# Iterate through triangular numbers until the desired number of digits is reached
for i in range(1, n):
triangular_number = (i * (i + 1)) // 2
if len(str(triangular_number)) == n:
return i
# If the loop ends without finding a suitable triangular number, return None
return None
# Test the function
assert find_Index(2) == 4
solar-10.7b-instruct. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
triangular_numbers = [sum(range(1, i + 1)) for i in range(1, 100)]
return next(i for i, number in enumerate(triangular_numbers) if len(str(number)) == n)
assert find_Index(2) == 4
gemma-2b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
if n == 1:
return 0
else:
return (n - 1) * (n - 1) + find_Index(n - 1)
claude-3-sonnet-20240229. fail_base: False, fail_plus: True
```python
import math
def find_Index(n):
"""
Find the index of the smallest triangular number with n digits.
Args:
n (int): The number of digits in the desired triangular number.
Returns:
int: The index of the smallest triangular number with n digits.
"""
# Initialize the index to 1
index = 1
# Keep incrementing the index until the triangular number has n digits
while True:
# Calculate the triangular number for the current index
triangular_num = (index * (index + 1)) // 2
# Check if the triangular number has n digits
if len(str(triangular_num)) == n:
return index
# Increment the index
index += 1
# Test cases
starcoder2-15b-oci. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# Your code here
pass
```
The function `find_Index` takes an integer `n` as input and returns the index of the smallest triangular number with `n` digits. The triangular numbers are generated using a loop and the index is incremented each time a new triangular number is generated. The loop stops when a triangular number with `n` digits is found. The index of the triangular number is then returned.
To test the function, I will use the provided assert statement to check if the function returns the correct index for the given input. If the function returns the correct index, the assertion will pass. If the function returns an incorrect index, the assertion will fail and an error message will be displayed.
Let's execute the code to see if it passes the test.
```python
def find_Index(n):
index = 1
triangular_number = 1
while len(str(triangular_number)) < n:
index += 1
triangular_number += index
return index
starcoder2-3b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
def find_Index(n):
# Your code here
return 0
print(find_Index(2))
print(find_Index(3))
print(find_Index(4))
print(find_Index(5))
print(find_Index(6))
print(find_Index(7))
print(find_Index(8))
print(find_Index(9))
print(find_Index(10))
print(find_Index(11))
print(find_Index(12))
print(find_Index(13))
print(find_Index(14))
print(find_Index(15))
print(find_Index(16))
print(find_Index(17))
print(find_Index(18))
print(find_Index(19))
print(find_Index(20))
print(find_Index(21))
print(find_Index(22))
print(find_Index(23))
print(find_Index(24))
print(find_Index(25))
print(find_Index(26))
print(find_Index(27))
print(find_Index(28))
print(find_Index(29))
print(find_Index(30))
print(find_Index(31))
print(find_Index(32))
print(find_Index(33))
print(find_Index(34))
print(find_Index(35))
print(find_Index(36))
print(find_Index(37))
print(find_Index(38))
print(find_Index(39))
print(find_Index(40))
print(find_Index(41))
print(find_Index(42))
print(find_Index(43))
print(find_Index(44))
print(find_Index(45))
print(find_Index(46))
print(find_Index(47))
print(find_Index(48))
print(find_Index(49))
print(find_Index(50))
print(find_Index(51))
print
speechless-starcoder2-15b. fail_base: True, fail_plus: True
def find_Index(n):
if n == 1:
return 1
else:
start = 10 ** (n - 1)
end = 10 ** n
for i in range(start, end):
if (i * (i + 1)) // 2 >= 10 ** (n - 1):
return i
return -1
assert find_Index(2) == 4
gemma-7b. fail_base: True, fail_plus: True
"""
Write a python function to find the index of smallest triangular number with n digits. https://www.geeksforgeeks.org/index-of-smallest-triangular-number-with-n-digits/
assert find_Index(2) == 4
"""
import math
def find_Index(n):
if n == 1:
return 1
if n == 2:
return 4
if n == 3:
return 10
if n == 4:
return 19
if n == 5:
return 31
if n == 6:
return 51
if n == 7:
return 81
if n == 8:
return 122
if n == 9:
return 184
if n == 10:
return 279
if n == 11:
return 411
if n == 12:
return 601
if n == 13:
return 861
if n == 14:
return 1221
if n == 15:
return 1691
if n == 16:
return 2361
if n == 17:
return 3231
if n == 18:
return 4391
if n == 19:
return 5911
if n == 20:
return 8011
if n == 21:
return 10811
if n == 22:
return 14411
if n == 23:
return 19111
if n == 24:
return 25111
if n == 25:
return 32911
if n == 26:
return 42511
if n == 27:
return 55111
if n == 28:
return 71111
if n == 29:
return 91911
if n == 30:
return 118111
if n == 31:
opencodeinterpreter-ds-6.7b. fail_base: False, fail_plus: True
```python
def find_Index(n):
if n == 1:
return 1
else:
index = 1
digits = 1
while digits < n:
index += 1
digits = len(str(index*(index+1)//2))
return index
# Test the function
print(find_Index(2))