A322005 Least prime p such that n + p is a Fibonacci number (A000045).

2, 2, 3, 2, 17, 3, 2, 137, 5, 601, 3, 2, 43, 131, 7, 19, 5, 17, 3, 2, 967, 13, 67, 11, 31, 927372692193078999151, 29, 7, 61, 5, 59, 3, 2, 577, 199, 109, 19, 107, 17, 571, 193, 103, 13, 101, 11, 2539, 43, 97, 7, 14930303, 5, 27777890035237, 3, 2, 179, 89, 6709, 10889, 31, 46309, 29, 83, 6703, 547, 313, 79, 23, 46301, 919, 541, 19, 73, 17

Offset: 0

Author

M. F. Hasler, Dec 12 2018

Keywords

• nonn

Comments

See A322004 for the indices of the corresponding Fibonacci numbers, and further information.

Examples

			a(0) = 2 is the smallest prime p such that p + 0 (= 2) is a Fibonacci number.
a(1) = 2 is the smallest prime p such that p + 1 (= 3) is a Fibonacci number.
a(2) = 3 is the smallest prime p such that p + 2 (= 5) is a Fibonacci number.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1958

Crossrefs

Cf. A000040, A000045, A322004.

Programs

Maple

f:= proc(n) local p,k,a,b,c;
a:= -n:b:= 1-n:
do
  c:= b;
  b:= a+b+n;
  a:= c;
  if isprime(b) then return b fi
od
end proc:
map(f, [$0..80]); # Robert Israel, Dec 14 2018

Mathematica

primeQ[n_] := n>0 && PrimeQ[n]; a[n_] := Module[{i=2}, While[!primeQ[Fibonacci[i] - n], i++]; Fibonacci[i] - n]; Array[a, 27, 0] (* Amiram Eldar, Dec 12 2018 *)

PARI

a(n)=for(i=1,oo,ispseudoprime(fibonacci(i)-n)&&return(fibonacci(i)-n))