cp's OEIS Frontend

A353929 Number of distinct sums of runs (of 0's or 1's) in the binary expansion of n.

%I A353929 #15 Jun 27 2022 01:08:59
%S A353929 1,1,2,1,2,2,2,1,2,2,2,3,2,3,2,1,2,2,2,3,2,2,3,3,2,3,3,2,2,3,2,1,2,2,
%T A353929 2,3,2,2,3,3,2,2,2,3,3,3,3,3,2,3,3,2,3,3,2,3,2,3,3,3,2,3,2,1,2,2,2,3,
%U A353929 2,2,3,3,2,2,2,3,3,3,3,3,2,2,2,3,2,2,3
%N A353929 Number of distinct sums of runs (of 0's or 1's) in the binary expansion of n.
%C A353929 Assuming the binary digits are not all 1, this is one more than the number of different lengths of runs of 1's in the binary expansion of n.
%H A353929 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/q/87559">What is a sequence run? (answered 2011-12-01)</a>
%e A353929 The binary expansion of 183 is (1,0,1,1,0,1,1,1), with runs (1), (0), (1,1), (0), (1,1,1), with sums 1, 0, 2, 0, 3, of which four are distinct, so a(183) = 4.
%t A353929 Table[Length[Union[Total/@Split[IntegerDigits[n,2]]]],{n,0,100}]
%o A353929 (Python)
%o A353929 from itertools import groupby
%o A353929 def A353929(n): return len(set(sum(map(int,y[1])) for y in groupby(bin(n)[2:]))) # _Chai Wah Wu_, Jun 26 2022
%Y A353929 For lengths of all runs we have A165413, firsts A165933.
%Y A353929 Numbers whose binary expansion has distinct runs are A175413.
%Y A353929 For runs instead of run-sums we have A297770, firsts A350952.
%Y A353929 For prime indices we have A353835, weak A353861, firsts A006939.
%Y A353929 For standard compositions we have A353849, firsts A246534.
%Y A353929 Positions of first appearances are A353930.
%Y A353929 A005811 counts runs in binary expansion.
%Y A353929 A044813 lists numbers with distinct run-lengths in binary expansion.
%Y A353929 A318928 gives runs-resistance of binary expansion.
%Y A353929 A351014 counts distinct runs in standard compositions.
%Y A353929 Cf. A215203, A353743, A353832, A353847, A353932, A354579.
%K A353929 base,nonn
%O A353929 0,3
%A A353929 _Gus Wiseman_, Jun 26 2022