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Numbers that can be written from base 2 to base 9 using only the digits 0 to 3.
6

%I #23 May 03 2019 08:40:29

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

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

%C Conjectured to be complete.

%C Checked up to 2^16384 (≈ 1.2*10^4932) on Oct 31 2008. - _Daniel Mondot_, Jan 17 2016

%C Checked up to 2^65520 (≈ 3*10^19723) on Nov 13 2008. - _Daniel Mondot_, Jan 17 2016

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

%H Stuart A. Burrell, Han Yu, <a href="https://arxiv.org/abs/1905.00832">Digit expansions of numbers in different bases</a>, arXiv:1905.00832 [math.NT], 2019.

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

%Y cf. A146025, A146027, A131646, A275600

%K nonn,base

%O 1,3

%A _Daniel Mondot_, Oct 27 2008