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%I #11 Feb 26 2024 09:13:41
%S 2,25,252,2525,25252,252525,2525252,25252525,252525252,2525252525,
%T 25252525252,252525252525,2525252525252,25252525252525,
%U 252525252525252,2525252525252525,25252525252525252,252525252525252525,2525252525252525252,25252525252525252525
%N The base 8 expansion of the number of trailing zeros of the base 8 expansion of (8^n)!.
%H Antonio M. Oller-Marcén and José María Grau, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Oller/oller3.html">On the base-b expansion of the number of trailing zeros of (b^k)!</a>, Journal of Integer Sequences, Vol 14. (11.6.7) 2011.
%t Z[p_, n_] := (n - H[p, n])/(p - 1); H[p_, n_] := {a = IntegerDigits[n, p]; bb = Length[a]; Sum[a[[i]], {i, bb}]}[[1]]; Z[p_, r_, n_] := Floor[Z[p, n]/r]; ZZ[b_, n_] := {aa = FactorInteger[b]; Min[Table[Z[aa[[i, 1]], aa[[i, 2]], n], {i, Length[aa]}]]}[[1]]; Table[ FromDigits@IntegerDigits[ZZ[8, 8^n], 8], {n, 15}]
%Y Cf. A174970, A173228.
%K nonn,base
%O 1,1
%A _José María Grau Ribas_, Oct 05 2013
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