A177461 The smallest k such that Fibonacci(n)+k and Fibonacci(n)-k are both prime.

0, 0, 0, 3, 0, 2, 3, 12, 0, 5, 0, 24, 3, 4, 0, 33, 48, 28, 57, 192, 0, 31, 12, 60, 81, 28, 0, 177, 108, 50, 345, 150, 168, 35, 6, 618, 735, 76, 18, 147, 0, 134, 111, 126, 0, 85, 642, 1146, 225, 92, 480, 219, 348, 466, 345, 72, 300, 89, 90, 312, 2025, 664, 168, 945, 276, 128

Offset: 3

Author

Vladimir Joseph Stephan Orlovsky, May 09 2010

Keywords

• nonn

Comments

Indices where a(n)= 0 are provided by A001605.

Examples

			3 +- 0 -> primes, 5 +- 0 -> primes, 8 +- 3 -> primes, 13 +- 0 -> primes, 21 +- 2 -> primes, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 3..1251

Crossrefs

Cf. A000045, A001605, A047160.

Programs

Maple

A047160 := proc(n) for k from 0 to n-1 do if isprime(n-k) and isprime(n+k) then return k; end if; end do: return -1 ; end proc:
A177461 := proc(n) A047160(combinat[fibonacci](n)) ; end proc: # R. J. Mathar, Jan 23 2011

Mathematica

f[n_] := Block[{k}, If[n==2||OddQ[n], k=0, k=1]; While[!PrimeQ[n-k] || !PrimeQ[n+k], k+=2]; k]; Table[f[Fibonacci[n]], {n,3,100}]

Formula

a(n) = A047160(A000045(n)). - R. J. Mathar, Jan 23 2011