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

1,4

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).

Links

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

Formula

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

Example

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).

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 *)

Prog

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

Crossrefs

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

Sequence in context: A261634 A295848 A226785 * A316989 A135009 A092747

Adjacent sequences: A245971 A245972 A245973 * A245975 A245976 A245977

Keyword

nonn,easy

Author

Wayne VanWeerthuizen, Aug 08 2014

Status

approved