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%I #36 Feb 24 2024 01:08:24
%S 3,5,23,37,97,157,1741,11933,50549,214129,560597,16276621,180510493,
%T 398386576261,1042989597313,41305516996050613,174972977841043309,
%U 13300248193487978669,238663270054423392193,624828552868675407173
%N Primes occurring in the sequence 3, 1, 4, 5, 9, 14, 23, ... (A000285 prefixed with 3).
%C Primes of the form F(k) + L(k+1), where F(k) and L(k) are the k-th Fibonacci number and Lucas number, respectively. - _Rigoberto Florez_, Jul 31 2022
%C a(36) has 852 digits, a(37) has 1052. - _Michael S. Branicky_, Jul 31 2022
%H Michael S. Branicky, <a href="/A091157/b091157.txt">Table of n, a(n) for n = 1..36</a>
%H Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, <a href="https://arxiv.org/abs/2211.10788">Primes and composites in the determinant Hosoya triangle</a>, arXiv:2211.10788 [math.NT], 2022.
%t Join[{3},Select[#[[1]]+#[[6]]&/@Partition[Fibonacci[ Range[ 0,200]],6,1],PrimeQ]] (* _Harvey P. Dale_, Sep 05 2021 *)
%o (Python)
%o from sympy import isprime, fibonacci as F, lucas as L
%o print([3]+list(filter(isprime, (F(k)+L(k+1) for k in range(1, 101)))))
%o # _Michael S. Branicky_, Jul 31 2022
%Y Cf. A091158, A000285.
%Y Cf. A000062, A000045.
%K nonn
%O 1,1
%A _G. L. Honaker, Jr._, Dec 23 2003
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