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 A258044 Fibonacci numbers that can be expressed as sum of 2 consecutive prime numbers. 2
 5, 8, 144, 1548008755920 (list; graph; refs; listen; history; text; internal format)
 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 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 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 KEYWORD nonn AUTHOR Abhiram R Devesh, May 17 2015 STATUS approved

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Last modified September 19 13:56 EDT 2020. Contains 337178 sequences. (Running on oeis4.)