A188195 Base-3 Keith numbers.

3, 5, 6, 7, 57, 102, 127, 206, 217, 677, 805, 840, 1486, 1680, 1887, 2090, 2834, 8329, 10145, 12866, 21127, 23002, 50782, 67925, 82685, 96841, 153861, 178852, 357896, 3826652, 17985694, 38610616, 38610808, 70587766, 160804168, 341014432, 632582224, 10267031505

Offset

1,1

Comments

Keith numbers are described in A007629.

Links

Amiram Eldar, Table of n, a(n) for n = 1..46

Example

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.

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[#, 3]&]

Crossrefs

Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188196-A188200 (bases 4 and 6-9).

Sequence in context: A179220 A290577 A145736 * A337092 A021741 A201906

Adjacent sequences: A188192 A188193 A188194 * A188196 A188197 A188198

Keyword

nonn,base

Author

T. D. Noe, Mar 24 2011

Extensions

a(38) from Amiram Eldar, Jan 20 2026

Status

approved