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A297778 Number of distinct runs in base-10 digits of n. 3

%I

%S 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,

%T 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,

%U 2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2

%N Number of distinct runs in base-10 digits of n.

%C Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences. A043562(n) = a(n) for n=1..100, but not for n=101.

%H Clark Kimberling, <a href="/A297778/b297778.txt">Table of n, a(n) for n = 1..10000</a>

%e 14! in base-10: 2,7,0,0,1,7,3,0,1,3,0,0; ten runs, of which 6 are distinct, so that a(14!) = 6.

%t b = 10; s[n_] := Length[Union[Split[IntegerDigits[n, b]]]]

%t Table[s[n], {n, 1, 200}]

%Y Cf. A043562 (number of runs, not necessarily distinct), A297770.

%K nonn,base,easy

%O 1,10

%A _Clark Kimberling_, Feb 03 2018

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Last modified May 6 09:45 EDT 2021. Contains 343580 sequences. (Running on oeis4.)