A385175 Cubes using at most three distinct digits, not ending in 0.

1, 8, 27, 64, 125, 216, 343, 512, 729, 1331, 2744, 3375, 46656, 238328, 778688, 1030301, 5177717, 7077888, 9393931, 700227072, 1003003001, 44474744007, 1000300030001, 1000030000300001, 1331399339931331, 3163316636166336, 1000003000003000001, 1000000300000030000001, 1000000030000000300000001

Offset: 1

Author

Gonzalo Martínez, Jun 20 2025

Keywords

• nonn
• base

Comments

This sequence has infinitely many terms since (10^m + 1)^3 is a term for all m >= 0.

Conjecture: a(26) = 3163316636166336 is the largest term with nonzero digits (See comments of A030294 and the data of A155146, where a(26) = A155146(47)^3).

Examples

			8, 343, and 46656 belong to this list because they are cubes that use 1, 2, and 3 distinct digits, respectively.
		

Crossrefs

Cf. A000578, A030292, A155146, A018884, A202940.

Programs

Mathematica

Select[Range[10^6]^3,Length[Union[IntegerDigits[#]]]<4&&IntegerDigits[#][[-1]]!=0&] (* James C. McMahon, Jun 30 2025 *)
fQ[n_] := Mod[n, 10] > 0 && Length@ Union@ IntegerDigits[n^3] < 4; k = 1; lst = {}; While[k < 1000002, If[ fQ@k, AppendTo[lst, k]]; k++]; lst^3 (* Robert G. Wilson v, Jul 10 2025 *)

Formula

a(n) = A202940(n)^3.

Extensions

a(28) from Robert G. Wilson v, Jul 10 2025

a(29) from David A. Corneth, Jul 10 2025