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

1,2

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).

Links

Table of n, a(n) for n=1..29.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A062292 A030295 A052045 * A014187 A050750 A100571

Adjacent sequences: A385172 A385173 A385174 * A385176 A385177 A385178

Keyword

nonn,base

Author

Gonzalo Martínez, Jun 20 2025

Extensions

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

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

Status

approved