cp's OEIS Frontend

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

%I A382728 #13 Aug 13 2025 21:48:59
%S A382728 1,3,6,10,15,21,28,36,45,55,66,78,91,93,97,103,111,121,133,147,163,
%T A382728 181,201,223,247,273,276,282,291,303,318,336,357,381,408,438,471,507,
%U A382728 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
%N A382728 Total number of entries in rows 0,1,...,n of Pascal's triangle not divisible by 13.
%H A382728 Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, <a href="https://arxiv.org/abs/2408.06817">Periodic minimum in the count of binomial coefficients not divisible by a prime</a>, arXiv:2408.06817 [math.NT], 2024.
%o A382728 (Python)
%o A382728 from math import prod
%o A382728 from gmpy2 import digits
%o A382728 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
%o A382728 (Python)
%o A382728 from math import prod
%o A382728 from gmpy2 import digits
%o A382728 def A382728(n):
%o A382728     d = list(map(lambda x:int(x,13)+1,digits(n+1,13)[::-1]))
%o A382728     return sum((b-1)*prod(d[a:])*91**a for a, b in enumerate(d))>>1 # _Chai Wah Wu_, Aug 13 2025
%Y A382728 Cf. A001316, A006046-A006048, A194458, A194459, A382720-A382731.
%K A382728 nonn
%O A382728 0,2
%A A382728 _N. J. A. Sloane_, Apr 23 2025