A030294 Numbers k such that k^3 has at most three different digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 30, 36, 40, 62, 70, 92, 100, 101, 110, 173, 192, 200, 211, 300, 400, 700, 888, 1000, 1001, 1010, 1100, 1920, 2000, 3000, 3543, 4000, 7000, 8880, 10000, 10001, 10010, 10100, 11000, 19200, 20000, 30000, 35430, 40000, 70000, 88800, 100000, 100001

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

While almost all larger terms have a regular digit pattern, there is the exception a(63) = 146796, a(63)^3 = A030295(63) = 3163316636166336. Are there other terms of this type? - Hugo Pfoertner, Feb 11 2020

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..130

Crossrefs

Cf. A030295.

Programs

Magma

[n: n in [0..400000] | #Set(Intseq(n^3)) le 3]; // Vincenzo Librandi, Nov 10 2014

Mathematica

d3Q[n_]:=Count[DigitCount[n^3],?(#>0&)]<4; Select[Range[0,110000],d3Q] (* _Harvey P. Dale, Mar 10 2016 *)
Select[Range[0,101000],Count[DigitCount[#^3],0]>6&] (* Harvey P. Dale, May 05 2023 *)

PARI

for(n=0,10^9+1,if(#Set(digits(n^3))<=3,print1(n,", "))); \\ Joerg Arndt, Dec 13 2014