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 A338314 #12 Feb 26 2025 06:27:37 %S A338314 4,8,76,104,116,296,872,1112,1378,2204,2774,2834,3016,4472,5174,5624, %T A338314 6364,6554,8854,9164,9976,10564,11026,11324,11476,12644,14356,14456, %U A338314 15124,15544,15688,16484,20492,20786,21944,26506,26564,30302,31996,32264,33368,35048 %N A338314 Even composite integers m such that A004254(m)^2 == 1 (mod m). %C A338314 If p is a prime, then A004254(p)^2 == 1 (mod p). %C A338314 This sequence contains the even composite integers for which the congruence holds. %C A338314 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. For a=5, b=1, U(n) recovers A004254(m). %C A338314 These numbers may be called weak generalized Lucas pseudoprimes of parameters a and b. The current sequence is defined for a=5 and b=1. %D A338314 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020). %H A338314 D. Andrica and O. Bagdasar, <a href="https://repository.derby.ac.uk/download/32debb6fc2f467a8ae693b090be6c47767b0dd2577af43223423ac8a70edf260/272814/MJOM-D-19-01391-Final%20%28corrected%29.pdf">On some new arithmetic properties of the generalized Lucas sequences</a>, Mediterr. J. Math. (2021). %t A338314 Select[Range[2, 15000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &] %Y A338314 Cf. A004254, A337782 (a=3), A337783 (a=7). %K A338314 nonn %O A338314 1,1 %A A338314 _Ovidiu Bagdasar_, Oct 22 2020 %E A338314 More terms from _Amiram Eldar_, Oct 22 2020