%I #19 Mar 20 2020 23:32:26
%S 1,0,140608,1000,4096000,140608000,1000000,4096000000,140608000000,
%T 1000000000,4096000000000,140608000000000,1000000000000,
%U 4096000000000000,140608000000000000,1000000000000000,4096000000000000000,140608000000000000000,1000000000000000000,4096000000000000000000,140608000000000000000000,1000000000000000000000
%N Smallest cube containing exactly n 0's.
%C 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
%F 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
%t nsmall = Table[Infinity, 20];
%t For[i = 0, i <= 10^6, i++, n0 = Count[IntegerDigits[i^3], 0];
%t If[nsmall[[n0 + 1]] > i^3, nsmall[[n0 + 1]] = i^3]];
%t Cases[nsmall, _?NumberQ] (* _Robert Price_, Mar 20 2020 *)
%Y Cf. A269250, A086008, A048365.
%Y Cf. A036528 - A036536 for other digits 1 - 9.
%Y Analog for squares: A036507 = A048345^2.
%K nonn,base
%O 0,3
%A _David W. Wilson_
%E Extended to a(0) = 1 and three lines of data completed by _M. F. Hasler_, Feb 20 2016