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

%I A258044 #38 Jul 29 2020 05:10:36
%S A258044 5,8,144,1548008755920
%N A258044 Fibonacci numbers that can be expressed as sum of 2 consecutive prime numbers.
%C A258044 The indices of these Fibonacci numbers are: 5, 6, 12, 60, 750, 8505, ...
%C A258044 a(5) was found by Carlos Rivera.
%C A258044 a(6) was found by Jan van Delden.
%C A258044 Conjecture: This list is finite.
%C A258044 Intersection of A000045 and A001043. - _Michel Marcus_, May 23 2015
%H A258044 Jinyuan Wang, <a href="/A258044/b258044.txt">Table of n, a(n) for n = 1..5</a>
%H A258044 Carlos Rivera, <a href="http://primepuzzles.net/puzzles/puzz_787.htm">Puzzle 787. Fibonacci as sum of two consecutive primes</a>, The Prime Puzzles and Problems Connection.
%e A258044 a(1) =   5 =  2 + 3;
%e A258044 a(2) =   8 =  3 + 5;
%e A258044 a(3) = 144 = 71 + 73;
%e A258044 a(4) = 1548008755920 = 774004377953 + 774004377967.
%o A258044 (Python)
%o A258044 from sympy import nextprime as np
%o A258044 from sympy import prevprime as pp
%o A258044 f1=1
%o A258044 f2=1
%o A258044 f3=f1+f2
%o A258044 while f3>0:
%o A258044     if f3%2==0 and f3>3:
%o A258044         i=f3/2
%o A258044         p=pp(i); q=np(p)
%o A258044         if p+q==f3:
%o A258044             print(f3)
%o A258044     f1=f2; f2=f3
%o A258044     f3=f1+f2
%Y A258044 Cf. A000045 (Fibonacci numbers), A001043 (sums of 2 successive primes).
%K A258044 nonn
%O A258044 1,1
%A A258044 _Abhiram R Devesh_, May 17 2015