A124067 -id:A124067 - cp's OEIS frontend

A363533 Least k such that n*F(k)+1 is prime, where F = A000045 is the Fibonacci sequence, or -1 if no such k exists.

1, 1, 3, 1, 3, 1, 9, 3, 3, 1, 3, 1, 9, 3, 3, 1, 6, 1, 9, 3, 3, 1, 3, 4, 18, 3, 9, 1, 3, 1, 15, 4, 3, 4, 3, 1, 9, 5, 3, 1, 3, 1, 48, 3, 9, 1, 24, 3, 9, 3, 3, 1, 3, 3, 9, 3, 6, 1, 24, 1, 36, 5, 3, 4, 3, 1, 12, 3, 3, 1, 6, 1, 12, 3, 3, 4, 6, 1, 9, 4, 3, 1, 3, 5

Offset: 1

Pontus von Brömssen, Jun 09 2023

nonn

2 does not appear because F(1) = F(2).

a(n) is divisible by 3 if n >= 3 is odd (unless a(n) = -1), because F(k) is odd (so n*F(k)+1 > 2 is even) when k is not divisible by 3.

			For n = 17, the least k such that 17*F(k)+1 is prime is k = 6, with 17*F(6)+1 = 17*8+1 = 137, so a(17) = 6.

Cf. A000045, A034693, A124067, A361902, A362376, A363534 (records), A363535 (indices of records), A363536 (first occurrences).

Array[(k = 1; While[! PrimeQ[# Fibonacci[k] + 1], k++]; k) &, 85] (* Michael De Vlieger, Jun 10 2023 *)

a(n) = my(k=1); while(!isprime(n*fibonacci(k)+1), k++); k; \\ Michel Marcus, Jun 10 2023

from sympy import isprime, fibonacci
from itertools import count
def A363533(n):
    # Note: the function hangs if a(n) = -1.
    return next(k for k in count(1) if isprime(n*fibonacci(k)+1))

a(n) = 1 if and only if n+1 is prime.

A124081 Primes of the form 2*F(k) + 1.

Original entry on oeis.org

3, 5, 7, 11, 17, 43, 179, 467, 8363, 21893, 35423, 92737, 392837, 204668311, 1402817467, 40730022149, 8105479075763, 15080227609492692859, 100190602496116782278655832523, 26361745652748197675264382970030251614748343

Offset: 1

Giovanni Teofilatto, Dec 12 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..40

Cf. A000045, A124067.

Select[Fibonacci@Range[2,300]*2+1,PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

a(n) = 2*A000045(A124067(n+1)) + 1. - Amiram Eldar, Sep 19 2022

A228145 Numbers k such that 2*Fibonacci(k) - 1 is prime.

Original entry on oeis.org

3, 4, 8, 9, 10, 16, 18, 31, 34, 39, 41, 42, 55, 68, 79, 90, 95, 97, 114, 122, 148, 151, 160, 209, 265, 320, 329, 441, 457, 516, 529, 632, 640, 682, 712, 791, 1056, 1169, 1632, 1943, 2200, 2279, 2468, 2698, 2921, 2996, 3129, 3140, 3656, 3960, 4889, 5560, 5895

Offset: 1

Vincenzo Librandi, Aug 13 2013

nonn

Jorge Coveiro, Table of n, a(n) for n = 1..62 (first 55 terms from Vincenzo Librandi)

Cf. A000045, A124067.

[n: n in [1..1700] | IsPrime(2*Fibonacci(n)-1)];

Select[Range[2000], PrimeQ[2 Fibonacci[#] - 1]&]

is(n)=ispseudoprime(2*fibonacci(n)-1) \\ Charles R Greathouse IV, Jun 13 2017

cp's OEIS Frontend

A363533 Least k such that n*F(k)+1 is prime, where F = A000045 is the Fibonacci sequence, or -1 if no such k exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A124081 Primes of the form 2*F(k) + 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A228145 Numbers k such that 2*Fibonacci(k) - 1 is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

PARI