A187713 - OEIS

%I #21 Jan 20 2026 08:44:51

%S 5,9,10,11,13,15,20,22,31,40,43,53,62,71,84,93,124,154,221,483,3044,

%T 18748,125973,232085,1705260,2091605,5616236,8067806,8849508,58944155,

%U 84572166,164487062,421825427,469435978,744740232,2034565620,8998799859,15062362054,30267276276

%N Base-5 Keith numbers.

%C 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.

%H Amiram Eldar, <a href="/A187713/b187713.txt">Table of n, a(n) for n = 1..42</a>

%e 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.

%e The number 14 is a Keith number in base 10 but not base 5, as we have: 2, 4, 6, 10, 16, ...

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

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

%K nonn,base

%O 1,1

%A _Alonso del Arte_, Mar 17 2011

%E Extended by _T. D. Noe_, Mar 23 2011

%E a(36)-a(39) from _Amiram Eldar_, Jan 20 2026