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 A339127 Odd composite integers m such that A087130(m-J(m,29)) == 2*J(m,29) (mod m), where J(m,29) is the Jacobi symbol. 8
 9, 25, 27, 49, 81, 121, 169, 175, 225, 243, 289, 325, 361, 529, 637, 729, 961, 1225, 1331, 1369, 1539, 1681, 1849, 2025, 2209, 2809, 3025, 3481, 3721, 4225, 4489, 5041, 5329, 5929, 6241, 6721, 6889, 6929, 7921, 8281, 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*J(p,D) (mod p) when p is prime, b=-1 and D=a^2+4. This sequence has the odd composite integers with V(m-J(m,D)) == 2*J(m,D) (mod m). For a=5 and b=-1, we have D=29 and V(m) recovers A087130(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 MATHEMATICA Select[Range[3, 10000, 2], CompositeQ[#] && Divisible[LucasL[# - (j = JacobiSymbol[#, 29]), 5] - 2*j, #] &] (* Amiram Eldar, Nov 26 2020 *) CROSSREFS Cf. A087130. Cf. A339125 (a=1, b=-1), A339126 (a=3, b=-1), A339128 (a=7, b=-1), A339129 (a=3, b=1), A339130 (a=5, b=1), A339131 (a=7, b=1). Sequence in context: A319165 A319152 A244623 * A117580 A280609 A340238 Adjacent sequences:  A339124 A339125 A339126 * A339128 A339129 A339130 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Nov 24 2020 STATUS approved

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Last modified June 14 12:26 EDT 2021. Contains 345025 sequences. (Running on oeis4.)