A382728 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 13.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 93, 97, 103, 111, 121, 133, 147, 163, 181, 201, 223, 247, 273, 276, 282, 291, 303, 318, 336, 357, 381, 408, 438, 471, 507, 546, 550, 558, 570, 586, 606, 630, 658, 690, 726, 766, 810, 858, 910, 915, 925, 940, 960, 985, 1015, 1050, 1090, 1135, 1185, 1240, 1300, 1365, 1371, 1383, 1401

Offset: 0

Author

N. J. A. Sloane, Apr 23 2025

Keywords

• nonn

Links

• Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Periodic minimum in the count of binomial coefficients not divisible by a prime, arXiv:2408.06817 [math.NT], 2024.

Crossrefs

Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.

Programs

Python

from math import prod
from gmpy2 import digits
def A382728(n): return sum(prod(int(d,13)+1 for d in digits(m,13)) for m in range(n+1)) # Chai Wah Wu, Aug 10 2025

Python

from math import prod
from gmpy2 import digits
def A382728(n):
    d = list(map(lambda x:int(x,13)+1,digits(n+1,13)[::-1]))
    return sum((b-1)*prod(d[a:])*91**a for a, b in enumerate(d))>>1 # Chai Wah Wu, Aug 13 2025