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 A339730 Odd composite integers m such that A056854(3*m-J(m,45)) == 47 (mod m) and gcd(m,45)=1, where J(m,45) is the Jacobi symbol. 3
 49, 161, 287, 323, 329, 341, 377, 451, 671, 737, 901, 1007, 1079, 1081, 1127, 1271, 1363, 1541, 1819, 1853, 1891, 1927, 2033, 2071, 2303, 2407, 2431, 2461, 2501, 2567, 2743, 3653, 3827, 4181, 4843, 5029, 5243, 5473, 5611, 5671, 5777, 6119, 6593, 6601, 6721, 6923 (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 V(k*p-J(p,D)) == V(k-1) (mod p) whenever p is prime, k is a positive integer, b=1 and D=a^2-4. The composite integers m with the property V(k*m-J(m,D)) == V(k-1) (mod m) are called generalized Pell-Lucas pseudoprimes of level k+ and parameter a. Here b=1, a=7, D=45 and k=3, while V(m) recovers A056854(m), with V(2)=47. 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 Amiram Eldar, Table of n, a(n) for n = 1..1000 Dorin Andrica, Vlad Crişan, and Fawzi Al-Thukair, On Fibonacci and Lucas sequences modulo a prime and primality testing, Arab Journal of Mathematical Sciences, 2018, 24(1), 9--15. MATHEMATICA Select[Range[3, 7000, 2], CoprimeQ[#, 45] && CompositeQ[#] && Divisible[LucasL[4*(3*# - JacobiSymbol[#, 45])] - 47, #] &] CROSSREFS Cf. A056854, A071904, A339131 (a=7, b=1, k=1), A339523 (a=7, b=1, k=2). Cf. A339728 (a=3, b=1), A339729 (a=5, b=1). Sequence in context: A159247 A265423 A226146 * A338011 A066551 A134210 Adjacent sequences: A339727 A339728 A339729 * A339731 A339732 A339733 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Dec 14 2020 STATUS approved

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Last modified September 28 23:23 EDT 2023. Contains 365739 sequences. (Running on oeis4.)