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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Apart from the initial 3, primes of the form F(k) + F(k+5), where F(k) is a Fibonacci number. - Paolo P. Lava, Jul 19 2012

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

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Last modified February 4 13:47 EST 2023. Contains 360055 sequences. (Running on oeis4.)