A245974 Tower of 7's mod n.

0, 1, 1, 3, 3, 1, 0, 7, 7, 3, 2, 7, 6, 7, 13, 7, 12, 7, 7, 3, 7, 13, 20, 7, 18, 19, 16, 7, 1, 13, 19, 23, 13, 29, 28, 7, 34, 7, 19, 23, 26, 7, 7, 35, 43, 43, 37, 7, 0, 43, 46, 19, 11, 43, 13, 7, 7, 1, 7, 43, 6, 19, 7, 55, 58, 13, 63, 63, 43, 63, 66, 7, 30

Offset: 1

Author

Wayne VanWeerthuizen, Aug 08 2014

Keywords

• nonn
• easy

Comments

a(n) = (7^(7^(7^(7^(7^ ... ))))) mod n, provided sufficient 7's are in the tower such that adding more doesn't affect the value of a(n).

Examples

			a(2) = 1, as 7^X is odd for any whole number X.
a(11) = 2, as 7^(7^7) == 7^(7^(7^7)) == 7^(7^(7^(7^7))) == 2 (mod 11).
		

Links

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

Crossrefs

Cf. A240162, A245970, A245971, A245972, A245973.

Programs

Maple

A:= proc(n) option remember; 7 &^ A(numtheory:-phi(n)) mod n end proc:
A(2):= 1;
seq(A(n), n=2..100);

Mathematica

a[n_] := a[n] = Switch[n, 1, 0, 2, 1, _, 7^a[EulerPhi[n]]]~Mod~n;
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 21 2022 *)

Sage

def a(n):
    if ( n <= 10 ):
        return 823543%n
    else:
        return power_mod(7,a(euler_phi(n)),n)

Formula

a(n) = 7^a(A000010(n)) mod n. For n <= 10, a(n) = (7^7) mod n.