A245971 Tower of 4s mod n.

0, 0, 1, 0, 1, 4, 4, 0, 4, 6, 4, 4, 9, 4, 1, 0, 1, 4, 9, 16, 4, 4, 3, 16, 21, 22, 13, 4, 24, 16, 4, 0, 4, 18, 11, 4, 34, 28, 22, 16, 37, 4, 41, 4, 31, 26, 17, 16, 11, 46, 1, 48, 47, 40, 26, 32, 28, 24, 45, 16, 57, 4, 4, 0, 61, 4, 55, 52, 49, 46, 50, 40, 37

Offset: 1

Author

Wayne VanWeerthuizen, Aug 08 2014

Keywords

• nonn
• easy

Comments

a(n) = (4^(4^(4^(4^(4^ ... ))))) mod n, provided sufficient 4s 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

Crossrefs

Cf. A240162, A245970, A245972, A245973, A245974.

Cf. A000010, A000302.

Programs

Haskell

import Math.NumberTheory.Moduli (powerMod)
a245971 n = powerMod 4 (phi + a245971 phi) n
            where phi = a000010 n
-- Reinhard Zumkeller, Feb 01 2015

Sage

def tower4mod(n):
    if n <= 10:
        return 256%n
    else:
        ep = euler_phi(n)
        return power_mod(4,ep+tower4mod(ep),n)
[tower4mod(n) for n in range(1, 30)]