A048365 a(n)^3 is smallest cube containing exactly n 0's.

1, 0, 52, 10, 160, 520, 100, 1600, 5200, 1000, 16000, 52000, 10000, 160000, 520000, 100000, 1600000, 5200000, 1000000, 16000000, 52000000, 10000000, 160000000, 520000000, 100000000, 1600000000, 5200000000, 1000000000

Offset: 0

Author

Patrick De Geest, Mar 15 1999

Keywords

• nonn
• base
• more

Comments

a(n) is the index of the first occurrence of n in A269250.-- Is there an index n = 3k+1 or n = 3k+2 from which on the pattern a(3k+1) = 16*10^k resp. a(3k+2) = 52*10^k is no longer true? - M. F. Hasler, Feb 20 2016

Links

• Eric Weisstein's World of Mathematics, Cubic Number

Crossrefs

Cf. A036527, A269250.

Programs

Mathematica

nsmall = Table[Infinity, 12];
For[i = 0, i <= 52000, i++, n0 = Count[IntegerDigits[i^3], 0];
  If[nsmall[[n0]] > i, nsmall[[ n0]] = i]];
Join[{1}, nsmall]  (* Robert Price, Sep 26 2018 *)

Formula

a(3k) = 10^k; a(3k+1) <= 16*10^k (k>0), a(3k+2) <= 52*10^k. - M. F. Hasler, Feb 20 2016

Extensions

a(19)-a(27) from Lars Blomberg, Jun 12 2011