A188200 Base-9 Keith numbers.

17, 21, 25, 42, 67, 81, 96, 101, 149, 162, 173, 202, 243, 303, 324, 346, 404, 405, 486, 519, 567, 648, 692, 732, 857, 1189, 1464, 2199, 4398, 11644, 18325, 33774, 34453, 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

Offset

1,1

Comments

Keith numbers are described in A007629. Base 9 appears to be unusually rich in Keith numbers. Why?

Links

Table of n, a(n) for n=1..58.

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

Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188195-A188199.

Sequence in context: A282109 A307863 A128546 * A060875 A259555 A138600

Adjacent sequences: A188197 A188198 A188199 * A188201 A188202 A188203

Keyword

nonn,base

Author

T. D. Noe, Mar 24 2011

Status

approved