This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A222759 #12 Nov 02 2024 03:21:47
%S A222759 0,2,1,0,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,2,2,2,2,2,2,2,2,
%T A222759 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A222759 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A222759 Conjectured number of primes p for which binomial(n*p,p) (mod p^3) does not equal n.
%C A222759 It appears that, for k > 2 and n >= prime(prime(k)^3), then a(n) >= k.
%C A222759 Sequences A000720 and A056811 give results for binomial(n*p,p) (mod p) and binomial(n*p,p) (mod p^2), respectively. It appears that mod p^3 is the last case; that is, this identity does not hold for higher powers. - _T. D. Noe_, Mar 14 2013
%H A222759 T. D. Noe, <a href="/A222759/b222759.txt">Table of n, a(n) for n = 1..10000</a>
%t A222759 Table[Length[Select[Prime[Range[100]], Mod[Binomial[n*#,#], #^3] != n &]], {n, 87}]
%Y A222759 Cf. A096328 (prime(prime(n)^3)).
%Y A222759 Cf. A000720, A056811 (primePi(n) and primePi(sqrt(n))).
%K A222759 nonn
%O A222759 1,2
%A A222759 _T. D. Noe_, Mar 12 2013