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A091157
Primes occurring in the sequence 3, 1, 4, 5, 9, 14, 23, ... (A000285 prefixed with 3).
3
3, 5, 23, 37, 97, 157, 1741, 11933, 50549, 214129, 560597, 16276621, 180510493, 398386576261, 1042989597313, 41305516996050613, 174972977841043309, 13300248193487978669, 238663270054423392193, 624828552868675407173
OFFSET
1,1
COMMENTS
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
a(36) has 852 digits, a(37) has 1052. - Michael S. Branicky, Jul 31 2022
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..36
Hsin-Yun Ching, Rigoberto Flórez, F. Luca, Antara Mukherjee, and J. C. Saunders, Primes and composites in the determinant Hosoya triangle, arXiv:2211.10788 [math.NT], 2022.
MATHEMATICA
Join[{3}, Select[#[[1]]+#[[6]]&/@Partition[Fibonacci[ Range[ 0, 200]], 6, 1], PrimeQ]] (* Harvey P. Dale, Sep 05 2021 *)
PROG
(Python)
from sympy import isprime, fibonacci as F, lucas as L
print([3]+list(filter(isprime, (F(k)+L(k+1) for k in range(1, 101)))))
# Michael S. Branicky, Jul 31 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
G. L. Honaker, Jr., Dec 23 2003
STATUS
approved