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%I #5 Mar 30 2012 17:22:57
%S 17,21,25,42,67,81,96,101,149,162,173,202,243,303,324,346,404,405,486,
%T 519,567,648,692,732,857,1189,1464,2199,4398,11644,18325,33774,34453,
%U 37999,70348,92664,141557,256820,263412,326778,349484,526824,535754,579708,1461987,1519308,1621052,2688905,4650964,8027458,8198651,8374956,13504910,17858551,20002383,55640285,154513633,170801638
%N Base-9 Keith numbers.
%C Keith numbers are described in A007629. Base 9 appears to be unusually rich in Keith numbers. Why?
%e 101 is here because, in base 9, 101 is 122 and applying the Keith iteration to this number produces the numbers 1, 2, 2, 5, 9, 16, 30, 55, 101. Note that the multiples 202, 303, and 404 are here also.
%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[#,9]&]
%Y Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188195-A188199.
%K nonn,base
%O 1,1
%A _T. D. Noe_, Mar 24 2011