A375751 a(n) is the difference between F=A000045(n) and the largest prime not exceeding F.

0, 0, 0, 1, 0, 2, 3, 2, 0, 5, 0, 4, 3, 4, 0, 5, 4, 2, 7, 4, 0, 17, 8, 14, 31, 14, 0, 37, 20, 26, 9, 20, 22, 11, 6, 12, 15, 32, 18, 17, 0, 16, 43, 24, 0, 17, 20, 26, 27, 20, 6, 9, 12, 34, 29, 36, 30, 47, 48, 4, 45, 32, 54, 27, 132, 22, 31, 4, 32, 11, 12, 60, 7, 76

Offset: 3

Author

Hugo Pfoertner, Aug 27 2024

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 3..10000

Crossrefs

Cf. A000045, A007917, A001605, A138184, A138185, A159977, A159978, A202090.

Programs

Maple

a:= n-> (F-> F-prevprime(F+1))(combinat[fibonacci](n)):
seq(a(n), n=3..76);  # Alois P. Heinz, Aug 27 2024

Mathematica

a[n_]:=Module[{p=2},While[(f=Fibonacci[n])>=p, pold=p;p=NextPrime[p]]; d=f-pold;If[d>0,f-pold,d=0]; d]; Array[a,74,3] (* Stefano Spezia, Aug 27 2024 *)
Map[(# - NextPrime[# + 1, -1]) &, Fibonacci[Range[3, 76]]] (* Amiram Eldar, Aug 29 2024 *)

PARI

a(n) = my(F=fibonacci(n)); F-precprime(F)

Python

from sympy import prevprime, fibonacci
def A375753(n): return (F:=fibonacci(n)) - prevprime(F+1) # Karl-Heinz Hofmann, Aug 27 2024

Formula

a(n) = A000045(n) - A138184(n).

a(n) = 0 <=> n in { A001605 }. - Alois P. Heinz, Aug 27 2024