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A043562
Number of runs in base-10 representation of n.
7
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
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
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
KEYWORD
nonn,base,easy
STATUS
approved