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Base-4 Keith numbers.
1

%I #7 Mar 30 2012 17:22:57

%S 5,7,10,15,18,29,47,113,163,269,1150,1293,1881,22173,44563,95683,

%T 261955,1179415,1295936,11451171,26867679,42531919,247791599,

%U 429914163,445379527,560533869,619222313,2147478019,2971786617,3474640372

%N Base-4 Keith numbers.

%C Keith numbers are described in A007629.

%e 47 is here because, in base 4, 47 is 233 and applying the Keith iteration to this number produces the numbers 2, 3, 3, 8, 14, 25, 47.

%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[#,4]&]

%Y Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188195-A188200.

%K nonn,base

%O 1,1

%A _T. D. Noe_, Mar 24 2011