A036527 Smallest cube containing exactly n 0's.

1, 0, 140608, 1000, 4096000, 140608000, 1000000, 4096000000, 140608000000, 1000000000, 4096000000000, 140608000000000, 1000000000000, 4096000000000000, 140608000000000000, 1000000000000000, 4096000000000000000, 140608000000000000000, 1000000000000000000, 4096000000000000000000, 140608000000000000000000, 1000000000000000000000

Offset

0,3

Comments

a(n)^(1/3) = A048365(n) is the index of the first occurrence of n in A269250. -- For n = 3k, obviously a(n) = 10^n. The first terms for indices n = 3k+1 and n = 3k+2 equals 4096*10^3k resp. 140608*10^3k. Is there an index from where on this is no longer true? - M. F. Hasler, Feb 20 2016

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = A048365(n)^3; a(3n) = 10^(3n); a(3n+1) <= 4096*10^(3n) = (16*10^n)^3 for n>0; a(3n+2) <= 140608*10^(3n) = (52*10^n)^3, with equality for all known terms. - M. F. Hasler, Feb 20 2016

Mathematica

nsmall = Table[Infinity, 20];
For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 0];
  If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
Cases[nsmall, _?NumberQ] (* Robert Price, Mar 20 2020 *)

Crossrefs

Cf. A269250, A086008, A048365.

Cf. A036528 - A036536 for other digits 1 - 9.

Analog for squares: A036507 = A048345^2.

Sequence in context: A156409 A281583 A186613 * A250570 A252017 A203833

Adjacent sequences: A036524 A036525 A036526 * A036528 A036529 A036530

Keyword

nonn,base

Author

David W. Wilson

Extensions

Extended to a(0) = 1 and three lines of data completed by M. F. Hasler, Feb 20 2016

Status

approved