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 A339131 #12 Dec 07 2020 18:23:36 %S A339131 49,121,169,289,323,329,361,377,451,529,841,961,1081,1127,1369,1681, %T A339131 1819,1849,1891,2033,2209,2303,2809,3481,3653,3721,3751,3827,4181, %U A339131 4489,4901,4961,5041,5329,5491,5671,5777,6137,6241,6601,6721,6889,7381,7921,8149,8557,9409 %N A339131 Odd composite integers m such that A056854(m-J(m,45)) == 2 (mod m) and gcd(m,45)=1, where J(m,45) is the Jacobi symbol. %C A339131 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 %C A339131 V(p-J(p,D)) == 2 (mod p) when p is prime, b=1 and D=a^2-4. %C A339131 This sequence contains the odd composite integers with V(m-J(m,D)) == 2 (mod m). %C A339131 For a=7 and b=1, we have D=45 and V(m) recovers A056854(m). %D A339131 D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020. %D A339131 D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021) %D A339131 D. Andrica, O. Bagdasar, On generalized pseudoprimality of level k (submitted) %t A339131 Select[Range[3, 10000, 2], CoprimeQ[#, 45] && CompositeQ[#] && Divisible[LucasL[4*(# - JacobiSymbol[#, 45])] - 2, #] &] (* _Amiram Eldar_, Nov 26 2020 *) %Y A339131 Cf. A056854. %Y A339131 Cf. A339125 (a=1, b=-1), A339126 (a=3, b=-1), A339127 (a=5, b=-1), A339128 (a=7, b=-1), A339129 (a=3, b=1), A339130 (a=5, b=1). %K A339131 nonn %O A339131 1,1 %A A339131 _Ovidiu Bagdasar_, Nov 24 2020