A297624 Numbers k such that Fibonacci(2*k+1) and Fibonacci(2*k-1) are prime.

2, 3, 6, 216, 285

Offset

1,1

Comments

a(6) > 1622184 if it exists (see A001605). - Chai Wah Wu, Jan 23 2018

Links

Table of n, a(n) for n=1..5.

Formula

From Chai Wah Wu, Jan 23 2018: (Start)

a(n) = (A279795(n)-1)/2 = (A281087(n)+1)/2 = (A073340(2n-1)+1)/2.

For n > 1, a(n) == 0 mod 3 as otherwise Fibonacci(2*k+1) or Fibonacci(2*k-1) is even. (End)

Example

2 is in the sequence because F(3)=2 and F(5)=5 are prime.
6 is in the sequence because F(11)=89 and F(13)=233 are prime.

Maple

with(combinat, fibonacci): select(k -> isprime(fibonacci(2*k+1)) and isprime(fibonacci(2*k-1)), [$1..500]); # Muniru A Asiru, Jan 25 2018

Mathematica

Select[Range[0, 3000], PrimeQ[Fibonacci[2 # + 1]] && PrimeQ[Fibonacci[2 # - 1]] &]

Prog

(Magma) [n: n in [0..700] | IsPrime(Fibonacci(2*n+1)) and  IsPrime(Fibonacci(2*n-1))];
(PARI) isok(n) = isprime(fibonacci(2*n-1)) && isprime(fibonacci(2*n+1)); \\ Michel Marcus, Jan 08 2018
(Python)
from sympy import isprime
A297624_list, k, a, b, c, aflag = [], 1, 1, 1, 2, False
while k < 1000:
    cflag = isprime(c)
    if aflag and cflag:
        A297624_list.append(k)
    k, a, b, c, aflag = k + 1, c, b + c, b + 2*c, cflag # Chai Wah Wu, Jan 23 2018
(GAP) o := [];; for k in [1..500] do if IsPrime(Fibonacci(2*k+1)) and IsPrime(Fibonacci(2*k-1)) then Add(o, k); fi; od; A297624 := o; # Muniru A Asiru, Jan 25 2018

Crossrefs

Cf. A000045, A001605, A073340, A117517, A117595, A279795, A281087.

Sequence in context: A018734 A018755 A018769 * A015762 A015770 A093038

Adjacent sequences: A297621 A297622 A297623 * A297625 A297626 A297627

Keyword

nonn,more

Author

Vincenzo Librandi, Jan 08 2018

Status

approved