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

3,6

Links

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

Formula

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

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A339451 A111182 A178142 * A076427 A284152 A011024

Adjacent sequences: A375748 A375749 A375750 * A375752 A375753 A375754

Keyword

nonn,easy

Author

Hugo Pfoertner, Aug 27 2024

Status

approved