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 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. 8
 49, 121, 169, 289, 323, 329, 361, 377, 451, 529, 841, 961, 1081, 1127, 1369, 1681, 1819, 1849, 1891, 2033, 2209, 2303, 2809, 3481, 3653, 3721, 3751, 3827, 4181, 4489, 4901, 4961, 5041, 5329, 5491, 5671, 5777, 6137, 6241, 6601, 6721, 6889, 7381, 7921, 8149, 8557, 9409 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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-J(p,D)) == 2 (mod p) when p is prime, b=1 and D=a^2-4. This sequence contains the odd composite integers with V(m-J(m,D)) == 2 (mod m). For a=7 and b=1, we have D=45 and V(m) recovers A056854(m). REFERENCES D. Andrica, O. Bagdasar, Recurrent Sequences: Key Results, Applications and Problems. Springer, 2020. D. Andrica, O. Bagdasar, On some new arithmetic properties of the generalized Lucas sequences, Mediterr. J. Math. (to appear, 2021) D. Andrica, O. Bagdasar, On generalized pseudoprimality of level k (submitted) LINKS Table of n, a(n) for n=1..47. MATHEMATICA Select[Range[3, 10000, 2], CoprimeQ[#, 45] && CompositeQ[#] && Divisible[LucasL[4*(# - JacobiSymbol[#, 45])] - 2, #] &] (* Amiram Eldar, Nov 26 2020 *) CROSSREFS Cf. A056854. 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). Sequence in context: A084733 A338499 A227863 * A374290 A115557 A167718 Adjacent sequences: A339128 A339129 A339130 * A339132 A339133 A339134 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Nov 24 2020 STATUS approved

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Last modified July 19 10:32 EDT 2024. Contains 374392 sequences. (Running on oeis4.)