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A043567 Number of runs in base-15 representation of n.

%I A043567 #15 Apr 23 2021 21:53:53
%S A043567 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 A043567 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 A043567 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 A043567 Number of runs in base-15 representation of n.
%C A043567 Every positive integers occurs infinitely many times.  See A297770 for a guide to related sequences.
%H A043567 Antti Karttunen, <a href="/A043567/b043567.txt">Table of n, a(n) for n = 0..65537</a>
%e A043567 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 A043567 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 A043567 Table[Length@ Split@ IntegerDigits[n, 15], {n, 0, 105}] (* _Michael De Vlieger_, Oct 10 2017 *)
%o A043567 (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 A043567 Cf. A043289, A043542, A297783 (number of distinct runs), A297770.
%K A043567 nonn,base
%O A043567 0,16
%A A043567 _Clark Kimberling_
%E A043567 More terms from _Antti Karttunen_, Oct 10 2017
%E A043567 Updated by _Clark Kimberling_, Feb 04 2018