A043567 - OEIS

%I #15 Apr 23 2021 21:53:53

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,

%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2

%N Number of runs in base-15 representation of n.

%C Every positive integers occurs infinitely many times.  See A297770 for a guide to related sequences.

%H Antti Karttunen, <a href="/A043567/b043567.txt">Table of n, a(n) for n = 0..65537</a>

%e For n = 226, its base-15 representation is "101" as 226 = 1*(15^2) + 0*(15^1) + 1*(15^0). "101" has three runs, thus a(226) = 3.

%e For n = 482, its base-15 representation is "222" as 482 = 2*(15^2) + 2*(15^1) + 2*(15^0). "222" has just one run, thus a(482) = 1.

%t Table[Length@ Split@ IntegerDigits[n, 15], {n, 0, 105}] (* _Michael De Vlieger_, Oct 10 2017 *)

%o (Scheme) (define (A043567 n) (let loop ((n n) (runs 1) (pd (modulo n 15))) (if (zero? n) runs (let ((d (modulo n 15))) (loop (/ (- n d) 15) (+ runs (if (not (= d pd)) 1 0)) d))))) ;; _Antti Karttunen_, Oct 10 2017

%Y Cf. A043289, A043542, A297783 (number of distinct runs), A297770.

%K nonn,base

%O 0,16

%A _Clark Kimberling_

%E More terms from _Antti Karttunen_, Oct 10 2017

%E Updated by _Clark Kimberling_, Feb 04 2018