This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A043556 #13 Jul 13 2024 22:24:03
%S A043556 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 A043556 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 A043556 4,3,4,4,4,4,3,4,4,4,4,3,2,3,3,3,2,1,2,2,3,3
%N A043556 Number of runs in base-4 representation of n.
%C A043556 Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences.
%F A043556 a(n) << log n. In particular, a(n) <= log(n)/log(4) + 1. - _Charles R Greathouse IV_, Jul 13 2024
%t A043556 b = 4; s[n_] := Length[Split[IntegerDigits[n, b]]];
%t A043556 Table[s[n], {n, 1, 200}]
%o A043556 (Python)
%o A043556 from itertools import groupby
%o A043556 from sympy.ntheory import digits
%o A043556 def A043556(n): return len(list(groupby(digits(n,4)[1:]))) # _Chai Wah Wu_, Jul 13 2024
%Y A043556 Cf. A297772 (number of distinct runs), A297770.
%K A043556 nonn,base
%O A043556 0,5
%A A043556 _Clark Kimberling_
%E A043556 Updated by _Clark Kimberling_, Feb 03 2018