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

Offset: 1

Author

Alonso del Arte, Mar 17 2011

Keywords

• nonn
• base

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.

Examples

			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, ...
		

Crossrefs

Cf. A007629, base-10 Keith numbers; A162724, binary Keith numbers.

Programs

Mathematica

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

Extensions

Extended by T. D. Noe, Mar 23 2011