A146026 Numbers that can be written from base 2 to base 9 using only the digits 0 to 3.

0, 1, 2, 3, 8281, 8282, 8283

Offset: 1

Author

Daniel Mondot, Oct 27 2008

Keywords

• nonn
• base

Comments

Conjectured to be complete.

Checked up to 2^16384 (≈ 1.2*10^4932) on Oct 31 2008. - Daniel Mondot, Jan 17 2016

Checked up to 2^65520 (≈ 3*10^19723) on Nov 13 2008. - Daniel Mondot, Jan 17 2016

It is a plausible conjecture that there are no more terms, but this has not been proved. - N. J. A. Sloane, Nov 17 2017

Links

• Stuart A. Burrell, Han Yu, Digit expansions of numbers in different bases, arXiv:1905.00832 [math.NT], 2019.

Crossrefs

cf. A146025, A146027, A131646, A275600

Programs

Mathematica

Select[Range[0, 10^5], Function[n, Times @@ Boole@ Map[Max@ IntegerDigits[n, #] <= 3 &, Range[2, 9]] > 0]] (* Michael De Vlieger, Aug 15 2016 *)