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

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

Offset

0,3

Comments

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

Links

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

Formula

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

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

Prog

(Python)
from sympy import lucas
def A338889(n):
    a, b, c, d, a2, b2, c2, d2, m = 1, 1, 1, 0, 1, 0, 0, 1, int(lucas(lucas(n)))
    for x in bin(m-1)[2:]:
        e, f = b2*c2%m, a2+d2
        a2, b2, c2, d2 = (pow(a2, 2, m)+e)%m, b2*f%m, c2*f%m, (pow(d2, 2, m)+e)%m
        if x=='1':
            a2, b2, c2, d2 = (a2*a+b2*c)%m, (a2*b+b2*d)%m, (c2*a+d2*c)%m, (c2*b+d2*d)%m
    return (a2+(b2<<1))%m # Chai Wah Wu, Jul 01 2026

Crossrefs

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

Sequence in context: A179742 A285000 A321444 * A104608 A241499 A236774

Adjacent sequences: A338886 A338887 A338888 * A338890 A338891 A338892

Keyword

nonn

Author

Alois P. Heinz, Nov 14 2020

Status

approved