login
a(n) is the least positive integer k such that all digits of k are 0 or 1 in exactly n different bases B, where 2 <= B <= k; i.e., such that A068953(k)=n.
1

%I #12 Aug 02 2017 23:55:53

%S 2,3,4,9,30,81,4096,531441,16777216

%N a(n) is the least positive integer k such that all digits of k are 0 or 1 in exactly n different bases B, where 2 <= B <= k; i.e., such that A068953(k)=n.

%C Is every term except 30 a power of either 2 or 3?

%e For n=4: 9 written in bases 2 through 9 is 1001, 100, 21, 14, 13, 12, 11, 10. In 4 bases, namely 2, 3, 8 and 9, all digits are 0 or 1.

%t f[1]=0; f[k_] := Length[Select[Rest[Union[Divisors[k], Divisors[k-1]]], Max@@IntegerDigits[k, # ]==1&]]; a[n_] := For[k=1, True, k++, If[f[k]==n, Return[k]]]

%Y Cf. A068953.

%K more,base,nonn

%O 1,1

%A _Naohiro Nomoto_, Mar 28 2002

%E Edited by _Dean Hickerson_, Mar 31 2002