A263101 a(n) = F(F(n)) mod F(n), where F = Fibonacci = A000045.

0, 0, 1, 2, 0, 5, 12, 5, 33, 5, 1, 0, 232, 233, 55, 5, 1596, 2563, 1, 5, 987, 10946, 28656, 0, 0, 75025, 189653, 89, 1, 6765, 1, 5, 6765, 1, 9227460, 0, 24157816, 1, 63245985, 5, 1, 267914275, 433494436, 4181, 1134896405, 1, 2971215072, 0, 7778741816, 75025

Offset: 1

Author

Alois P. Heinz, Oct 09 2015

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000045, A002708, A007570, A076240, A127787 (where a(n)=0), A263112, A274996.

Programs

Maple

F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
p:= (M, n, k)-> map(x-> x mod k, `if`(n=0, <<1|0>, <0|1>>,
          `if`(n::even, p(M, n/2, k)^2, p(M, n-1, k).M))):
a:= n-> p(<<0|1>, <1|1>>, F(n)$2)[1, 2]:
seq(a(n), n=1..50);

Mathematica

F[n_] := MatrixPower[{{0, 1}, {1, 1}}, n][[1, 2]];
p[M_, n_, k_] := Mod[#, k]& /@ If[n == 0, {{1, 0}, {0, 1}}, If[EvenQ[n], MatrixPower[p[M, n/2, k], 2], p[M, n - 1, k].M]];
a[n_] := p[{{0, 1}, {1, 1}}, F[n], F[n]][[1, 2]];
Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Oct 29 2024, after Alois P. Heinz *)

PARI

alist(nn)= my(f=fibonacci); [ f(f(n))%f(n) |n<-[1..nn] ]; \\ Ruud H.G. van Tol, Dec 13 2024

Formula

a(n) = A007570(n) mod A000045(n).