A188196 Base-4 Keith numbers.

5, 7, 10, 15, 18, 29, 47, 113, 163, 269, 1150, 1293, 1881, 22173, 44563, 95683, 261955, 1179415, 1295936, 11451171, 26867679, 42531919, 247791599, 429914163, 445379527, 560533869, 619222313, 2147478019, 2971786617, 3474640372, 11753588964, 24452091777, 24453922692

Offset

1,1

Comments

Keith numbers are described in A007629.

Links

Table of n, a(n) for n=1..33.

Example

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.

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[#, 4]&]

Crossrefs

Cf. A007629 (base 10), A162724 (base 2), A187713 (base 5), A188195-A188200 (bases 3-4 and 6-9).

Sequence in context: A183044 A133756 A196936 * A381677 A048584 A085382

Adjacent sequences: A188193 A188194 A188195 * A188197 A188198 A188199

Keyword

nonn,base

Author

T. D. Noe, Mar 24 2011

Extensions

a(31)-a(33) from Amiram Eldar, Jan 20 2026

Status

approved