OFFSET
1,1
COMMENTS
Keith numbers are described in A007629. Base 9 appears to be unusually rich in Keith numbers. Why?
EXAMPLE
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.
MATHEMATICA
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]&]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
T. D. Noe, Mar 24 2011
STATUS
approved