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%I #8 Oct 24 2020 17:27:55
%S 4,8,76,104,116,296,872,1112,1378,2204,2774,2834,3016,4472,5174,5624,
%T 6364,6554,8854,9164,9976,10564,11026,11324,11476,12644,14356,14456,
%U 15124,15544,15688,16484,20492,20786,21944,26506,26564,30302,31996,32264,33368,35048
%N Even composite integers m such that A004254(m)^2 == 1 (mod m).
%C If p is a prime, then A004254(p)^2 == 1 (mod p).
%C This sequence contains the even composite integers for which the congruence holds.
%C 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 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 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (2020)
%D D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021)
%t Select[Range[2, 15000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 5/2]*ChebyshevU[#-1, 5/2] - 1, #] &]
%Y Cf. A337782 (a=3), A337783 (a=7).
%K nonn
%O 1,1
%A _Ovidiu Bagdasar_, Oct 22 2020
%E More terms from _Amiram Eldar_, Oct 22 2020