A091157 Primes occurring in the sequence 3, 1, 4, 5, 9, 14, 23, ... (A000285 prefixed with 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

Cf. A091158, A000285.

Cf. A000062, A000045.

Sequence in context: A238199 A296927 A215132 * A199336 A214876 A280273

Adjacent sequences: A091154 A091155 A091156 * A091158 A091159 A091160

Keyword

nonn

Author

G. L. Honaker, Jr., Dec 23 2003

Status

approved