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 A338310 Even composites m such that A086902(m)==7 (mod m). 0
 4, 8, 22, 88, 472, 5588, 10408, 20648, 34568, 123076, 1783976, 3677228, 4609418, 4857688, 6027208, 9906578, 16508152, 19995308, 20226572, 32039062, 56484004, 88835528, 97896692, 135858088, 354671468, 1091638108, 2260976428, 3495804596, 3723523516, 5577624308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If p is a prime, then A086902(p)==7 (mod p). This sequence contains the even composite integers for which the congruence holds. The generalized Pell-Lucas sequence 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) whenever p is prime and b=-1,1. For a=7, b=-1, V(m) recovers A086902(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) LINKS MATHEMATICA Select[Range[2, 25000, 2], CompositeQ[#] && Divisible[LucasL[#, 7] - 7, #] &] CROSSREFS Cf. A338079 (sequence of odd terms); A335668 (a=2). Sequence in context: A129788 A170938 A003684 * A254404 A254403 A075688 Adjacent sequences:  A338307 A338308 A338309 * A338311 A338312 A338313 KEYWORD nonn AUTHOR Ovidiu Bagdasar, Oct 22 2020 EXTENSIONS a(9)-a(15) from Amiram Eldar, Oct 22 2020 a(16)-a(30) from Daniel Suteu, Oct 22 2020 STATUS approved

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Last modified September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)