A030292 Numbers k such that k^3 has at most two different digits.

0, 1, 2, 3, 4, 7, 10, 11, 20, 100, 200, 1000, 2000, 10000, 20000, 100000, 200000, 1000000, 2000000, 10000000, 20000000, 100000000, 200000000, 1000000000, 2000000000, 10000000000, 20000000000

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• nice

Comments

Except for 0, 3, 4, 7, and 11, each term is of the form 10^x or 2*10^x. - Harvey P. Dale, Feb 05 2013

Programs

Magma

[n: n in [0..4000000] | #Set(Intseq(n^3)) le 2]; // Vincenzo Librandi, Nov 10 2014

Maple

filter:= n -> nops(convert(convert(n^3,base,10),set)) <= 2:
select(filter, [$1..10^5]); # Robert Israel, Nov 10 2014

Mathematica

Join[Select[Range[0,20],Count[DigitCount[#^3],0]>7&],Flatten[Table[{10^n,2*10^n},{n,2,10}]]] (* Harvey P. Dale, Nov 23 2019 *)

PARI

isok(n) = #Set(digits(n^3)) <= 2; \\ Michel Marcus, Nov 10 2014

Python

A030292_list, m = [0], [6, -6, 1, 0]
for n in range(1,10**6+1):
    for i in range(3):
        m[i+1] += m[i]
    if len(set(str(m[-1]))) <= 2:
        A030292_list.append(n) # Chai Wah Wu, Nov 05 2014

Extensions

More terms from Lior Manor, Jul 24 2001