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

%I A177461 #15 Oct 06 2023 04:47:46
%S A177461 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,
%T A177461 177,108,50,345,150,168,35,6,618,735,76,18,147,0,134,111,126,0,85,642,
%U A177461 1146,225,92,480,219,348,466,345,72,300,89,90,312,2025,664,168,945,276,128
%N A177461 The smallest k such that Fibonacci(n)+k and Fibonacci(n)-k are both prime.
%C A177461 Indices where a(n)= 0 are provided by A001605.
%H A177461 Robert Israel, <a href="/A177461/b177461.txt">Table of n, a(n) for n = 3..1251</a>
%F A177461 a(n) = A047160(A000045(n)). - _R. J. Mathar_, Jan 23 2011
%e A177461 3 +- 0 -> primes, 5 +- 0 -> primes, 8 +- 3 -> primes, 13 +- 0 -> primes, 21 +- 2 -> primes, ...
%p A177461 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:
%p A177461 A177461 := proc(n) A047160(combinat[fibonacci](n)) ; end proc: # _R. J. Mathar_, Jan 23 2011
%t A177461 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}]
%Y A177461 Cf. A000045, A001605, A047160.
%K A177461 nonn
%O A177461 3,4
%A A177461 _Vladimir Joseph Stephan Orlovsky_, May 09 2010