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 A338082 #8 Apr 28 2022 19:18:44 %S A338082 9,15,21,35,45,63,99,105,195,231,315,323,329,369,377,423,435,451,595, %T A338082 665,705,805,861,903,1081,1189,1443,1551,1819,1833,1869,1891,1935, %U A338082 2033,2211,2345,2465,2737,2849,2871,2961,3059,3289,3653,3689,3745,3827,4005,4059 %N A338082 Odd composite integers m such that A056854(m) == 7 (mod m). %C A338082 If p is a prime, then A056854(p)==7 (mod p). %C A338082 This sequence contains the odd composite integers for which the congruence holds. %C A338082 The generalized Pell-Lucas sequences of integer parameters (a,b) defined by V(m+2)=a*V(m+1)-b*V(m) and V(0)=2, V(1)=a, satisfy the identity V(p)==a (mod p) when p is prime and b=-1,1. %C A338082 For a=7 and b=1, V(m) recovers A056854(m). %D A338082 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020. %D A338082 D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021) %t A338082 Select[Range[3, 20000, 2], CompositeQ[#] && Divisible[2*ChebyshevT[#, 7/2] - 7, #] &] %t A338082 Select[Range[9,5001,2],CompositeQ[#]&&Mod[LucasL[4#],#]==7&] (* _Harvey P. Dale_, Apr 28 2022 *) %Y A338082 Cf. A005248, A335669 (a=3,b=-1), A335672 (a=3,b=1), A335673 (a=4,b=1), A335674 (a=5,b=1), A337233 (a=6,b=1). %K A338082 nonn %O A338082 1,1 %A A338082 _Ovidiu Bagdasar_, Oct 08 2020