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 A113305 #14 Mar 04 2024 08:51:25
%S A113305 2,5,11,13,23,29,31,37,53,59,61,67,71,79,83,89,97,101,103,127,137,139,
%T A113305 149,151,157,163,167,181,197,211,223,227,229,239,241,251,257,263,271,
%U A113305 313,317,331,337,349,353,359,367,379,389,397,431,433,449,461,463,479
%N A113305 Primes that do not divide any central trinomial coefficient, A002426.
%C A113305 For primes less than 10^6, the density of these primes is near 0.6075.
%H A113305 G. C. Greubel, <a href="/A113305/b113305.txt">Table of n, a(n) for n = 1..1600</a>
%H A113305 Nadav Kohen, <a href="https://arxiv.org/abs/2403.00149">Uniform Recurrence in the Motzkin Numbers and Related Sequences mod p</a>, arXiv:2403.00149 [math.CO], 2024.
%H A113305 Narad Rampersad and Jeffrey Shallit, <a href="https://arxiv.org/abs/2110.06244">Congruence properties of combinatorial sequences via Walnut and the Rowland-Yassawi-Zeilberger automaton</a>, arXiv:2110.06244 [math.CO], 2021.
%t A113305 nn=1000; a=b=1; t=Join[{1}, Table[c=((2n-1)b+3(n-1)a)/n; a=b; b=c; c, {n, 2, nn}]]; pLst={}; Do[p=Prime[n]; k=1; While[k<p && Mod[t[[k]], p]>0, k++ ]; If[k==p, AppendTo[pLst, p]], {n, PrimePi[nn]}]; pLst
%Y A113305 Cf. A113302 (number of k for which prime(n) divides T(k)), A113303 (least k such that prime(n) divides T(k)).
%K A113305 nonn
%O A113305 1,1
%A A113305 _T. D. Noe_, Oct 24 2005