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Final nonzero digit of n^n in base 16.
3

%I #33 Oct 02 2024 17:13:55

%S 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,

%T 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,

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

%N Final nonzero digit of n^n in base 16.

%C The sequence is periodic with period length 16.

%H Jose María Grau and A. M. Oller-Marcen, <a href="http://arxiv.org/abs/1203.4066">On the last digit and the last non-zero digit of n^n in base b</a>, arXiv:1203.4066 [math.NT], 2012.

%H Jose María Grau and A. M. Oller-Marcen, <a href="http://pdf.medrang.co.kr/kms01/BKMS/51/BKMS-51-5-1325-1337.pdf">On the last digit and the last non-zero digit of n^n in base b</a>, Bull. Korean Math. Soc. 51 (2014), No. 5, pp. 1325-1337.

%t 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}]

%t 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 *)

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

%K nonn,base

%O 1,2

%A _José María Grau Ribas_, Feb 23 2014