OFFSET
1,1
COMMENTS
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.
LINKS
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.
EXAMPLE
a(1) = 5 = 2 + 3;
a(2) = 8 = 3 + 5;
a(3) = 144 = 71 + 73;
a(4) = 1548008755920 = 774004377953 + 774004377967.
PROG
(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
f3=f1+f2
CROSSREFS
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, May 17 2015
STATUS
approved