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A043562 Number of runs in base 10 representation of n. 5
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

COMMENTS

Blecksmith, Filaseta, & Nicol show that lim a(k^n) = infinity whenever k is not a power of 10. More generally, in base b, the limit is infinity exactly when log k/log b is irrational. - Charles R Greathouse IV, Jan 29 2014

Every positive integers occurs infinitely many times.  See A297770 for a guide to related sequences. - Clark Kimberling, Feb 04 2018

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..10000

Richard Blecksmith, Michael Filaseta, and Charles Nicol, A result on the digits of a^n, Acta Arithmetica 64 (1993), pp. 331-339.

MATHEMATICA

Table[Length[Split[IntegerDigits[n]]], {n, 0, 90}] (* Harvey P. Dale, Aug 24 2016 *)

PROG

(PARI) a(n)=my(d=digits(n)); #d-sum(i=2, #d, d[i]==d[i-1]) \\ Charles R Greathouse IV, Jan 29 2014

CROSSREFS

Cf. A297778 (number of distinct runs), A297770.

Sequence in context: A043536 A043561 A297778 * A043537 A047726 A297779

Adjacent sequences:  A043559 A043560 A043561 * A043563 A043564 A043565

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 23 04:30 EST 2019. Contains 320411 sequences. (Running on oeis4.)