A173228 -id:A173228 - cp's OEIS frontend

A174807 Floor(10^n/4) - A173228(n).

0, 1, 1, 1, 1, 2, 1, 1, 2, 3, 3, 3, 3, 2, 3, 4, 5, 5, 5, 4, 3, 5, 6, 7, 5, 8, 8, 6, 8, 10, 10, 8, 6, 7, 8, 8, 10, 7, 9, 9, 10, 11, 10, 9, 10, 9, 11, 11, 11, 11, 12, 13, 13, 12, 14, 10, 14, 17, 15, 13, 13, 12, 15, 14, 16, 15, 12, 14, 15, 15, 16, 15, 15, 15, 16, 13, 12, 16, 17, 14, 20, 20, 20

Offset: 1

José María Grau Ribas, Mar 29 2010

a(n) = A055223(n) if n>1.

Antonio M. Oller-Marcen, José María Grau, On the base b expansion of the number of trailing zeros of b^k!, arXiv:1002.4175 [math.NT], 2010, and J. Int. Seq. 14 (2011) 11.6.8

A229975 The base 8 expansion of the number of trailing zeros of the base 8 expansion of (8^n)!.

Original entry on oeis.org

2, 25, 252, 2525, 25252, 252525, 2525252, 25252525, 252525252, 2525252525, 25252525252, 252525252525, 2525252525252, 25252525252525, 252525252525252, 2525252525252525, 25252525252525252, 252525252525252525, 2525252525252525252, 25252525252525252525

Offset: 1

José María Grau Ribas, Oct 05 2013

Antonio M. Oller-Marcén and José María Grau, On the base-b expansion of the number of trailing zeros of (b^k)!, Journal of Integer Sequences, Vol 14. (11.6.7) 2011.

Cf. A174970, A173228.

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}]
Table[FromDigits[PadRight[{},n,{2,5}]],{n,20}] (* Harvey P. Dale, Oct 21 2024 *)

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A174807 Floor(10^n/4) - A173228(n).

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A229975 The base 8 expansion of the number of trailing zeros of the base 8 expansion of (8^n)!.

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