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

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, 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, 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

Offset: 1

Author

Robert Israel, Aug 22 2024

Keywords

• nonn

Examples

			a(5) = 3 because 5 - Fibonacci(0) = 5, 5 - Fibonacci(3) = 3 and 5 - Fibonacci(4) = 2 are prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A108852, A132144, A168383, A169791.

Programs

Maple

fcount:= proc(n) local f,i,d,c;
  c:= 0;
  for i from 0 do
    f:= combinat:-fibonacci(i);
    if f >= n then return c fi;
    if isprime(n-f) then
      c:= c+1;
    fi
  od;
end proc:
map(f, [$1..200]);

Mathematica

a[n_]:=Sum[Boole[PrimeQ[n-Fibonacci[i]]],{i,Select[Range[0,n],n>Fibonacci[#]&]}]; Array[a,99] (* Stefano Spezia, Aug 23 2024 *)