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
Links
- Amiram Eldar, Table of n, a(n) for n = 3..10000
Programs
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Maple
a:= n-> (F-> F-prevprime(F+1))(combinat[fibonacci](n)): seq(a(n), n=3..76); # Alois P. Heinz, Aug 27 2024
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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)
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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) = 0 <=> n in { A001605 }. - Alois P. Heinz, Aug 27 2024