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

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, 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, 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

Offset

0,16

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Example

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.
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.

Mathematica

Table[Length@ Split@ IntegerDigits[n, 15], {n, 0, 105}] (* Michael De Vlieger, Oct 10 2017 *)

Prog

(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

Crossrefs

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

Sequence in context: A043541 A297783 A043542 * A297784 A043568 A043543

Adjacent sequences: A043564 A043565 A043566 * A043568 A043569 A043570

Keyword

nonn,base

Author

Clark Kimberling

Extensions

More terms from Antti Karttunen, Oct 10 2017

Updated by Clark Kimberling, Feb 04 2018

Status

approved