A338889 -id:A338889 - cp's OEIS frontend

A274996 a(n) = F(F(F(n))) mod F(F(n)), where F = Fibonacci = A000045.

0, 0, 0, 1, 0, 5, 232, 987, 1, 5, 1, 0, 2211236406303914545699412969744873993387956988652, 2211236406303914545699412969744873993387956988653, 139583862445

Offset: 1

Alois P. Heinz, Nov 11 2016

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..19

Cf. A000045, A007570, A058051, A263101, A263112, A338889.

F:= 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[1, 2]
    end:
a:= n-> (h-> F(h$2))(F(F(n))):
seq(a(n), n=1..15);

a(n) = A058051(n) mod A007570(n).

A338736 a(n) = L(L(n)) mod n, where L = Lucas numbers = A000032.

Original entry on oeis.org

0, 0, 1, 1, 4, 0, 3, 7, 7, 4, 10, 3, 9, 10, 7, 15, 12, 0, 10, 9, 7, 4, 22, 3, 1, 4, 7, 1, 4, 18, 30, 31, 7, 4, 29, 15, 1, 34, 34, 39, 35, 24, 29, 29, 7, 4, 46, 3, 1, 4, 7, 29, 29, 0, 21, 55, 7, 54, 35, 3, 45, 4, 7, 63, 64, 36, 2, 29, 7, 4, 6, 3, 43, 4, 7, 29

Offset: 1

Alois P. Heinz, Nov 05 2020

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A000032, A005371, A263112, A338638, A338889.

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, n) mod n)(b(n)):
seq(a(n), n=1..80);

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

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

Original entry on oeis.org

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

Alois P. Heinz, Nov 04 2020

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

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

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);

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

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

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

cp's OEIS Frontend

A274996 a(n) = F(F(F(n))) mod F(F(n)), where F = Fibonacci = A000045.

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A338736 a(n) = L(L(n)) mod n, where L = Lucas numbers = A000032.

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Maple

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

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Maple

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