A258044 Fibonacci numbers that can be expressed as sum of 2 consecutive prime numbers.

5, 8, 144, 1548008755920

Offset: 1

Author

Abhiram R Devesh, May 17 2015

Keywords

• nonn

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.

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

Examples

			a(1) =   5 =  2 + 3;
a(2) =   8 =  3 + 5;
a(3) = 144 = 71 + 73;
a(4) = 1548008755920 = 774004377953 + 774004377967.
		

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.

Crossrefs

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

Programs

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