A245972 Tower of 5s mod n.

0, 1, 2, 1, 0, 5, 3, 5, 2, 5, 1, 5, 5, 3, 5, 5, 14, 11, 6, 5, 17, 1, 5, 5, 0, 5, 2, 17, 9, 5, 25, 21, 23, 31, 10, 29, 35, 25, 5, 5, 9, 17, 28, 1, 20, 5, 23, 5, 45, 25, 14, 5, 51, 29, 45, 45, 44, 9, 48, 5, 14, 25, 38, 53, 5, 23, 5, 65, 5, 45, 1, 29, 34, 35, 50

Offset

1,3

Comments

a(n) = (5^(5^(5^(5^(5^ ... ))))) mod n, provided sufficient 5s are in the tower such that adding more doesn't affect the value of a(n).

Links

Wayne VanWeerthuizen, Table of n, a(n) for n = 1..10000

Formula

a(n) = 5^a(A000010(n)) mod n. For n<=18, a(n)=(5^5) mod n.

Example

a(2) = 1, as 5^X is odd for any whole number X.
a(19) = 6, as 5^(5^5) == 5^(5^(5^5)) == 5^(5^(5^(5^5))) == 6 (mod 19).

Maple

A:= proc(n) option remember; 5 &^ A(numtheory:-phi(n)) mod n end proc:
A(2):= 1;
seq(A(n), n=2..100);

Mathematica

a[n_] := a[n] = PowerMod[5, If[n <= 18, 5, a[EulerPhi[n]]], n];
Array[a, 100] (* Jean-François Alcover, Jul 25 2022 *)

Prog

(Sage)
def a(n):
    if ( n <= 18 ):
        return 3125%n
    else:
        return power_mod(5, a(euler_phi(n)), n)

Crossrefs

Cf. A000010, A240162, A245970, A245971, A245973, A245974.

Sequence in context: A327358 A256664 A226783 * A088391 A128899 A155887

Adjacent sequences: A245969 A245970 A245971 * A245973 A245974 A245975

Keyword

nonn,easy

Author

Wayne VanWeerthuizen, Aug 08 2014

Status

approved