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A258044
Fibonacci numbers that can be expressed as sum of 2 consecutive prime numbers.
2
5, 8, 144, 1548008755920
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.
Intersection of A000045 and A001043. - Michel Marcus, May 23 2015
LINKS
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
Cf. A000045 (Fibonacci numbers), A001043 (sums of 2 successive primes).
Sequence in context: A356826 A267003 A151827 * A162571 A046490 A155214
KEYWORD
nonn
AUTHOR
Abhiram R Devesh, May 17 2015
STATUS
approved