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A043562
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Number of runs in base 10 representation of n.
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5
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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
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OFFSET
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0,11
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COMMENTS
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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
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LINKS
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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.
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MATHEMATICA
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Table[Length[Split[IntegerDigits[n]]], {n, 0, 90}] (* Harvey P. Dale, Aug 24 2016 *)
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PROG
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(PARI) a(n)=my(d=digits(n)); #d-sum(i=2, #d, d[i]==d[i-1]) \\ Charles R Greathouse IV, Jan 29 2014
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CROSSREFS
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Cf. A297778 (number of distinct runs), A297770.
Sequence in context: A043536 A043561 A297778 * A043537 A047726 A297779
Adjacent sequences: A043559 A043560 A043561 * A043563 A043564 A043565
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KEYWORD
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nonn,base,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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