A338638 -id:A338638 - cp's OEIS frontend

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

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.

A338889 a(n) = L(L(L(n))) mod L(L(n)), where L = Lucas numbers = A000032.

Original entry on oeis.org

1, 0, 3, 1, 1, 1, 0, 1, 1, 29, 7, 1, 19679776435706023589554718882448088434898811874077010905231927243854, 1, 7

Offset: 0

Alois P. Heinz, Nov 14 2020

nonn

a(21) = 2992285359..7163788371 has 5090 decimal digits.

Alois P. Heinz, Table of n, a(n) for n = 0..20

Cf. A000032, A005371, A262361, A274996, A338638, A338736.

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-> (h-> b(h$2) mod h)(b(b(n))):
seq(a(n), n=0..15);

a(n) = A262361(n) mod A005371(n).

cp's OEIS Frontend

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

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