A260031 Final nonzero digit of n^n in base 12.

1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 1, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 4, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 9, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 4, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 1, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 9, 1, 4, 3, 4, 5, 3, 7, 4, 9, 4, 11, 1

Offset: 1

Author

N. J. A. Sloane, Jul 19 2015

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• José María Grau and Antonio M. Oller-Marcén, On the last digit and the last non-zero digit of n^n in base b, arXiv preprint arXiv:1203.4066 [math.NT], 2012.

Crossrefs

Cf. A174824, A204819, A230024.

Cf. A000312, A010881.

Programs

Haskell

import Math.NumberTheory.Moduli (powerMod)
a260031 n = if x > 0 then x else f $ div (n ^ n) 12
          where x = powerMod n n 12
                f z = if m == 0 then f z' else m
                      where (z', m) = divMod z 12
-- Reinhard Zumkeller, Jul 19 2015

Python

from gmpy2 import mpz, digits
def A260031(n):
    s = digits(mpz(n)**mpz(n),12)
    t = s[-1]
    while t == '0':
        s = s[:-1]
        t = s[-1]
    return int(t,12) # Chai Wah Wu, Jul 19 2015

Extensions

More terms from Chai Wah Wu, Jul 19 2015