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

Author

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

Keywords

• nonn

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.

Crossrefs

Cf. A091158, A000285.

Cf. A000062, A000045.

Programs

Mathematica

Join[{3},Select[#[[1]]+#[[6]]&/@Partition[Fibonacci[ Range[ 0,200]],6,1],PrimeQ]] (* Harvey P. Dale, Sep 05 2021 *)

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