A187713 Base-5 Keith numbers.

5, 9, 10, 11, 13, 15, 20, 22, 31, 40, 43, 53, 62, 71, 84, 93, 124, 154, 221, 483, 3044, 18748, 125973, 232085, 1705260, 2091605, 5616236, 8067806, 8849508, 58944155, 84572166, 164487062, 421825427, 469435978, 744740232, 2034565620, 8998799859, 15062362054, 30267276276

Offset

1,1

Comments

Among bases b = 2 to 36, in b = 5 there is the third highest percentage of Keith numbers between b and b^3 (that is, numbers with two or three digits); only binary and ternary have more Keith numbers in that range.

Links

Amiram Eldar, Table of n, a(n) for n = 1..42

Example

a(2) = 9. In base 5, the number 9 is written 14, and the second order linear recurrence is then 1, 4, 5, 9, ... therefore 9 is a Keith number in base 5.
The number 14 is a Keith number in base 10 but not base 5, as we have: 2, 4, 6, 10, 16, ...

Mathematica

(* First run the program for A186830 to define keithSeq *) Select[Range[5, 10^6], Last[keithSeq[#, 5]] == # &]

Crossrefs

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

Sequence in context: A093711 A325204 A163670 * A101082 A277706 A300669

Adjacent sequences: A187710 A187711 A187712 * A187714 A187715 A187716

Keyword

nonn,base

Author

Alonso del Arte, Mar 17 2011

Extensions

Extended by T. D. Noe, Mar 23 2011

a(36)-a(39) from Amiram Eldar, Jan 20 2026

Status

approved