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Number of distinct runs in base-6 digits of n.
3

%I #4 Feb 03 2018 16:38:02

%S 1,1,1,1,1,2,1,2,2,2,2,2,2,1,2,2,2,2,2,2,1,2,2,2,2,2,2,1,2,2,2,2,2,2,

%T 1,2,2,3,3,3,3,2,1,2,2,2,2,3,2,2,3,3,3,3,2,3,2,3,3,3,2,3,3,2,3,3,2,3,

%U 3,3,2,2,3,2,3,3,3,3,2,2,3,3,3,2,2,1

%N Number of distinct runs in base-6 digits of n.

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

%H Clark Kimberling, <a href="/A297774/b297774.txt">Table of n, a(n) for n = 1..10000</a>

%e 9^9 in base-6: 1,0,2,2,3,5,4,3,3,2,1,3; ten runs, of which 8 are distinct, so that a(9^9) = 8.

%t b = 6; s[n_] := Length[Union[Split[IntegerDigits[n, b]]]]

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

%Y Cf. A043558 (number of runs, not necessarily distinct), A297770.

%K nonn,base,easy

%O 1,6

%A _Clark Kimberling_, Jan 27 2018