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Number of runs in base-4 representation of n.
4

%I #13 Jul 13 2024 22:24:03

%S 1,1,1,1,2,1,2,2,2,2,1,2,2,2,2,1,2,3,3,3,2,1,2,2,3,3,2,3,3,3,3,2,2,3,

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

%U 4,3,4,4,4,4,3,4,4,4,4,3,2,3,3,3,2,1,2,2,3,3

%N Number of runs in base-4 representation of n.

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

%F a(n) << log n. In particular, a(n) <= log(n)/log(4) + 1. - _Charles R Greathouse IV_, Jul 13 2024

%t b = 4; s[n_] := Length[Split[IntegerDigits[n, b]]];

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

%o (Python)

%o from itertools import groupby

%o from sympy.ntheory import digits

%o def A043556(n): return len(list(groupby(digits(n,4)[1:]))) # _Chai Wah Wu_, Jul 13 2024

%Y Cf. A297772 (number of distinct runs), A297770.

%K nonn,base

%O 0,5

%A _Clark Kimberling_

%E Updated by _Clark Kimberling_, Feb 03 2018