A230024 Final nonzero digit of n^n in base 16.

1, 4, 11, 1, 5, 4, 7, 1, 9, 4, 3, 1, 13, 4, 15, 1, 1, 4, 11, 1, 5, 4, 7, 1, 9, 4, 3, 1, 13, 4, 15, 1, 1, 4, 11, 1, 5, 4, 7, 1, 9, 4, 3, 1, 13, 4, 15, 1, 1, 4, 11, 1, 5, 4, 7, 1, 9, 4, 3, 1, 13, 4, 15, 1, 1, 4, 11, 1, 5, 4, 7, 1, 9, 4, 3, 1, 13, 4, 15, 1, 1

Offset: 1

Author

José María Grau Ribas, Feb 23 2014

Keywords

• nonn
• base

Comments

The sequence is periodic with period length 16.

Links

• Jose María Grau and A. M. Oller-Marcen, On the last digit and the last non-zero digit of n^n in base b, arXiv:1203.4066 [math.NT], 2012.
• Jose María Grau and A. M. Oller-Marcen, On the last digit and the last non-zero digit of n^n in base b, Bull. Korean Math. Soc. 51 (2014), No. 5, pp. 1325-1337.

Crossrefs

Cf. A116081, A204815-A204819, A230024, A204697.

Programs

Mathematica

f[n_, b_] := Module[{m = n^n}, While[Mod[m, b] == 0, m = m/b]; Mod[m, b]]; y = Table[f[i, 16], {i, 1, 100}]
Table[Drop[IntegerDigits[n^n,16],-IntegerExponent[n^n,16]][[-1]],{n,100}] (* or *) PadRight[{},100,{1,4,11,1,5,4,7,1,9,4,3,1,13,4,15,1}] (* Harvey P. Dale, Oct 02 2024 *)