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

Author

Wayne VanWeerthuizen, Aug 08 2014

Keywords

• nonn
• easy

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).

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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 *)

Sage

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

Formula

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