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A375642 a(n) is the number of i for which n - Fibonacci(i) is prime.

%I A375642 #14 Aug 23 2024 12:19:35
%S A375642 0,1,3,3,3,3,3,4,1,3,2,3,3,3,3,3,1,4,3,4,2,2,2,5,2,3,1,2,1,3,3,5,1,3,
%T A375642 0,3,3,3,3,2,2,4,2,5,3,2,2,3,2,3,2,2,2,3,2,2,2,3,1,4,3,5,2,3,1,3,2,4,
%U A375642 2,1,2,5,2,6,3,2,1,2,2,4,3,2,1,5,1,3,2,2,1,2,3,5,1,3,1,3,2,3,1
%N A375642 a(n) is the number of i for which n - Fibonacci(i) is prime.
%H A375642 Robert Israel, <a href="/A375642/b375642.txt">Table of n, a(n) for n = 1..10000</a>
%e A375642 a(5) = 3 because 5 - Fibonacci(0) = 5, 5 - Fibonacci(3) = 3 and 5 - Fibonacci(4) = 2 are prime.
%p A375642 fcount:= proc(n) local f,i,d,c;
%p A375642   c:= 0;
%p A375642   for i from 0 do
%p A375642     f:= combinat:-fibonacci(i);
%p A375642     if f >= n then return c fi;
%p A375642     if isprime(n-f) then
%p A375642       c:= c+1;
%p A375642     fi
%p A375642   od;
%p A375642 end proc:
%p A375642 map(f, [$1..200]);
%t A375642 a[n_]:=Sum[Boole[PrimeQ[n-Fibonacci[i]]],{i,Select[Range[0,n],n>Fibonacci[#]&]}]; Array[a,99] (* _Stefano Spezia_, Aug 23 2024 *)
%Y A375642 Cf. A000045, A108852, A132144, A168383, A169791.
%K A375642 nonn
%O A375642 1,3
%A A375642 _Robert Israel_, Aug 22 2024