A338638 a(n) = L(L(n)) mod L(n), where L = Lucas numbers = A000032.

1, 0, 1, 3, 1, 1, 0, 1, 1, 7, 4, 1, 199, 1, 4, 843, 1, 1, 0, 1, 29, 123, 4, 1, 3, 199, 4, 39603, 29, 1, 5778, 1, 1, 7, 4, 17622890, 12752043, 1, 4, 39603, 7881196, 1, 5778, 1, 29, 7, 4, 1, 3, 1149851, 28143689044, 7, 29, 1, 0, 312119004790, 6643838879, 7, 4, 1

Offset: 0

Author

Alois P. Heinz, Nov 04 2020

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4795

Crossrefs

Cf. A000032, A005371, A016089, A213060, A263101, A338736, A338889.

Programs

Maple

b:= proc(n) local r, M, p; r, M, p:=
      <<1|0>, <0|1>>, <<0|1>, <1|1>>, n;
      do if irem(p, 2, 'p')=1 then r:=
        `if`(nargs=1, r.M, r.M mod args[2]) fi;
         if p=0 then break fi; M:=
        `if`(nargs=1, M.M, M.M mod args[2])
      od; (r.<<2, 1>>)[1$2]
    end:
a:= n-> (f-> b(f$2) mod f)(b(n)):
seq(a(n), n=0..60);

Mathematica

Table[Mod[LucasL[LucasL[n]],LucasL[n]],{n,0,60}] (* Harvey P. Dale, Jul 04 2022 *)

Formula

a(n) = A005371(n) mod A000032(n).

a(n) = 0 for n in { A016089 }.