%I #7 Mar 30 2012 17:22:57
%S 3,5,6,7,57,102,127,206,217,677,805,840,1486,1680,1887,2090,2834,8329,
%T 10145,12866,21127,23002,50782,67925,82685,96841,153861,178852,357896,
%U 3826652,17985694,38610616,38610808,70587766,160804168,341014432,632582224
%N Base-3 Keith numbers.
%C Keith numbers are described in A007629.
%e 57 is here because, in base 3, 57 is 2010 and applying the Keith iteration to this number produces the numbers 2, 0, 1, 0, 3, 4, 8, 15, 30, 57.
%t IsKeith[n_,b_] := Module[{d, s, k}, d = IntegerDigits[n, b]; s = Total[d]; k = 1; While[AppendTo[d, s]; s = 2 s - d[[k]]; s < n, k++]; s == n]; Select[Range[3,10^5], IsKeith[#,3]&]
%Y Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188196-A188200.
%K nonn,base
%O 1,1
%A _T. D. Noe_, Mar 24 2011