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 A343533 #22 Apr 23 2021 06:38:26
%S A343533 2,3,3,1,3,3,0,3,3,0,3,1,0,3,3,0,0,3,0,3,3,0,3,1,0,3,0,0,3,3,0,0,3,0,
%T A343533 3,3,0,0,3,0,3,0,0,3,0,0,0,3,0,3,3,0,3,3,0,3,0,0,0,1,0,1,3,0,3,0,0,3,
%U A343533 3,0,0,0,0,3,3,0,0,3,0,0,3,0,3,1,0,3,0
%N A343533 a(n) is the largest value of k such that binomial(2*m-1, m-1) == 1 (mod m^k) for m = 2*n + 1.
%C A343533 If 2*n + 1 is a prime >= 5, then a(n) >= 3 by Wolstenholme's theorem.
%C A343533 If 2*n + 1 is a Wolstenholme prime (A088164), then a(n) >= 4.
%C A343533 If 2*n + 1 is a term of A267824, then a(n) >= 2.
%C A343533 If 2*n + 1 is the square of an odd prime, the cube of a prime >= 5 or a term of A228562, then a(n) >= 1.
%p A343533 a := proc(n) local x, x0, y, k, bound; bound := 1000;
%p A343533 x := 2*n + 1; x0 := x;
%p A343533 y := binomial(4*n + 1, 2*n);
%p A343533 for k from 0 to bound while y mod x = 1 do
%p A343533 x := x * x0 od;
%p A343533 if k < bound then k else print("No k below ", bound) fi end:
%p A343533 seq(a(n), n = 1..100); # _Peter Luschny_, Apr 22 2021
%o A343533 (PARI) a(n) = my(x=2*n+1, b=binomial(2*x-1, x-1)); for(k=1, oo, if(Mod(b, x^k)!=1, return(k-1)))
%Y A343533 Cf. A005408, A088164, A136327, A228562, A267824.
%K A343533 nonn
%O A343533 1,1
%A A343533 _Felix Fröhlich_, Apr 18 2021