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

3,4

Comments

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

Links

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

Formula

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

Example

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

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}]

Crossrefs

Cf. A000045, A001605, A047160.

Sequence in context: A001608 A159977 A245251 * A201924 A112974 A113069

Adjacent sequences: A177458 A177459 A177460 * A177462 A177463 A177464

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 09 2010

Status

approved