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 A338313 #15 Oct 24 2020 17:26:58 %S A338313 4,8,16,32,68,248,268,544,1328,4216,4768,9112,9376,12664,20128,22112, %T A338313 24536,25544,30488,43262,61574,125792,148004,304792,398248,493646, %U A338313 648848,913456,1036664,1975784,2350792,3672454,4248488,5422688,6318188,6768928,7079656,8560724 %N A338313 Even composite positive integers m such that A052918(m-1)^2 == 1 (mod m). %C A338313 If p is a prime, then A052918(p-1)^2 == 1 (mod p). %C A338313 This sequence contains the even composite integers for which the congruence holds. %C A338313 The generalized Lucas sequence of integer parameters (a,b) defined by U(m+2) = a*U(m+1)-b*U(m) and U(0)=0, U(1)=1, satisfies the identity U^2(p) == 1 (mod p) whenever p is prime and b=-1,1. %C A338313 For a=5, b=-1, U(m) recovers A052918(m-1), for m=1,2,.... %D A338313 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020) %D A338313 D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021) %t A338313 Select[Range[2, 20000, 2], CompositeQ[#] && Divisible[Fibonacci[#, 5]*Fibonacci[#, 5] - 1, #] &] %Y A338313 Cf. A337235 (a=3) %K A338313 nonn %O A338313 1,1 %A A338313 _Ovidiu Bagdasar_, Oct 22 2020 %E A338313 More terms from _Amiram Eldar_, Oct 22 2020 %E A338313 a(31)-a(38) from _Daniel Suteu_, Oct 22 2020