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 A373764 #4 Jun 22 2024 22:41:31
%S A373764 369,441,4473,10609,292559
%N A373764 Odd composite numbers k such that A086615(k-1) == 2*(-1)^((k-1)/2) (mod k).
%C A373764 The congruence holds for all odd primes.
%C A373764 a(6) > 2.3*10^7, if it exists.
%H A373764 Moa Apagodu and Doron Zeilberger, <a href="https://doi.org/10.4169/amer.math.monthly.124.7.597">Using the "Freshman's Dream" to Prove Combinatorial Congruences</a>, The American Mathematical Monthly, Vol. 124, No. 7 (2017), pp. 597-608; <a href="https://arxiv.org/abs/1606.03351">arXiv preprint</a>, arXiv:1606.03351 [math.CO], 2016.
%t A373764 seq[kmax_] := Module[{s0 = 1, s1 = 2, s2 = 4, s3, s = {}}, Do[s3 = (3*(k+1)*s2 + (k-4)*s1 - 3*(k-1)*s0)/(k+2); If[EvenQ[k] && !PrimeQ[k+1] && Divisible[s3 - 2*(-1)^(k/2), k+1], AppendTo[s, k+1]]; s0 = s1; s1 = s2; s2 = s3, {k, 3, kmax}]; s]; seq[500]
%o A373764 (PARI) lista(kmax) = {my(s0 = 1, s1 = 2, s2 = 4, s3); for(k = 3, kmax, s3 = (3*(k+1)*s2 + (k-4)*s1 - 3*(k-1)*s0)/(k+2); if(!(k % 2) && !isprime(k+1) && !((s3 - 2*(-1)^(k/2)) % (k+1)), print1(k+1, ", ")); s0 = s1; s1 = s2; s2 = s3);}
%Y A373764 Cf. A086615.
%K A373764 nonn,hard,more
%O A373764 1,1
%A A373764 _Amiram Eldar_, Jun 18 2024