A202940 -id:A202940 - cp's OEIS frontend

A308708 Numbers k such that k^3 contains exactly three distinct digits; numbers with trailing zeros are excluded.

5, 6, 8, 9, 14, 15, 36, 62, 92, 101, 173, 192, 211, 888, 1001, 3543, 10001, 100001, 110011, 146796, 1000001, 10000001, 100000001, 1000000001, 10000000001

Offset: 1

Andrej Jakobcic, Aug 01 2019

10^k + 1 (A000533(k)) is a term for k >= 2. - Jinyuan Wang, Aug 02 2019

			a(8) = 62 because 62^3 = 238328, which contains exactly three distinct digits.

Cf. A000533, A202940, A030294, A052051.

[k:k in [1..10000001]| k mod 10 ne 0 and  #Set(Intseq(k^3)) eq 3]; // Marius A. Burtea, Aug 02 2019

Select[Range[10001], Mod[#, 10] > 0 && Length@ Union@ IntegerDigits[#^3] == 3 &] (* Giovanni Resta, Sep 05 2019 *)

is(k) = #vecsort(digits(k^3), , 8)==3 && k%10!=0; \\ Jinyuan Wang, Aug 02 2019

More terms from Jinyuan Wang, Aug 02 2019

a(23)-a(25) from Jon E. Schoenfield, Aug 02 2019

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

Original entry on oeis.org

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

Gonzalo Martínez, Jun 20 2025

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).

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

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

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 *)

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

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

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

cp's OEIS Frontend

A308708 Numbers k such that k^3 contains exactly three distinct digits; numbers with trailing zeros are excluded.

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