A229975 The base 8 expansion of the number of trailing zeros of the base 8 expansion of (8^n)!.
2, 25, 252, 2525, 25252, 252525, 2525252, 25252525, 252525252, 2525252525, 25252525252, 252525252525, 2525252525252, 25252525252525, 252525252525252, 2525252525252525, 25252525252525252, 252525252525252525, 2525252525252525252, 25252525252525252525
Offset: 1
Links
- 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.
Programs
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Mathematica
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 *)