1,1

The indices of these Fibonacci numbers are: 5, 6, 12, 60, 750, 8505, ...

a(5) was found by Carlos Rivera.

a(6) was found by Jan van Delden.

Conjecture: This list is finite.

Intersection of A000045 and A001043. - Michel Marcus, May 23 2015

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

Carlos Rivera, Puzzle 787. Fibonacci as sum of two consecutive primes, The Prime Puzzles and Problems Connection.

a(1) = 5 = 2 + 3;

a(2) = 8 = 3 + 5;

a(3) = 144 = 71 + 73;

a(4) = 1548008755920 = 774004377953 + 774004377967.

(Python)

from sympy import nextprime as np

from sympy import prevprime as pp

f1=1

f2=1

f3=f1+f2

while f3>0:

if f3%2==0 and f3>3:

i=f3/2

p=pp(i); q=np(p)

if p+q==f3:

print(f3)

f1=f2; f2=f3

Cf. A000045 (Fibonacci numbers), A001043 (sums of 2 successive primes).

Sequence in context: A025518 A267003 A151827 * A162571 A046490 A155214

Adjacent sequences: A258041 A258042 A258043 * A258045 A258046 A258047

nonn

Abhiram R Devesh, May 17 2015

approved