cp's OEIS Frontend

A337783 Even composite integers m such that U(m)^2 == 1 (mod m), where U(m)=A004187(m) is the m-th generalized Lucas number of parameters a=7 and b=1.

%I A337783 #20 Nov 24 2023 12:39:09
%S A337783 4,8,16,44,104,136,152,164,176,232,286,442,496,656,836,856,976,1072,
%T A337783 1364,1378,1394,1804,1826,2204,2248,2584,2626,2684,2834,3016,3268,
%U A337783 3536,3926,4264,4346,4636,5084,5104,5146,5662,7208,7216,7384,7676,7964,8294,8632,8774,9164,9316,9976
%N A337783 Even composite integers m such that U(m)^2 == 1 (mod m), where U(m)=A004187(m) is the m-th generalized Lucas number of parameters a=7 and b=1.
%C A337783 This sequence contains the even composite integers for which the congruence holds.
%C A337783 The generalized Lucas sequences of integer parameters (a,b) defined by U(n+2)=a*U(n+1)-b*U(n) and U(0)=0, U(1)=1, satisfies the identity U^(p)==1 (mod p) whenever p is prime and b=-1,1.
%D A337783 D. Andrica and O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer (to appear, 2020).
%H A337783 D. Andrica and O. Bagdasar, <a href="https://repository.derby.ac.uk/item/92yqq/on-some-new-arithmetic-properties-of-the-generalized-lucas-sequences">On some new arithmetic properties of the generalized Lucas sequences</a>, preprint for Mediterr. J. Math. 18, 47 (2021).
%t A337783 Select[Range[2, 10000, 2], CompositeQ[#] && Divisible[ChebyshevU[#-1, 7/2]*ChebyshevU[#-1, 7/2] - 1, #] &]
%Y A337783 Cf. A337781 and A337782.
%K A337783 nonn
%O A337783 1,1
%A A337783 _Ovidiu Bagdasar_, Sep 20 2020
%E A337783 More terms from _Amiram Eldar_, Sep 21 2020