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A372515 Irregular triangle read by rows where row n lists the positions of zeros in the reversed binary expansion of n.

%I A372515 #7 May 29 2024 07:04:50
%S A372515 1,1,2,2,1,1,2,3,2,3,1,3,3,1,2,2,1,1,2,3,4,2,3,4,1,3,4,3,4,1,2,4,2,4,
%T A372515 1,4,4,1,2,3,2,3,1,3,3,1,2,2,1,1,2,3,4,5,2,3,4,5,1,3,4,5,3,4,5,1,2,4,
%U A372515 5,2,4,5,1,4,5,4,5,1,2,3,5,2,3,5,1,3,5
%N A372515 Irregular triangle read by rows where row n lists the positions of zeros in the reversed binary expansion of n.
%e A372515 The reversed binary expansion of 100 is (0,0,1,0,0,1,1), with zeros at positions {1,2,4,5}, so row 100 is (1,2,4,5).
%e A372515 Triangle begins:
%e A372515    1:
%e A372515    2: 1
%e A372515    3:
%e A372515    4: 1 2
%e A372515    5: 2
%e A372515    6: 1
%e A372515    7:
%e A372515    8: 1 2 3
%e A372515    9: 2 3
%e A372515   10: 1 3
%e A372515   11: 3
%e A372515   12: 1 2
%e A372515   13: 2
%e A372515   14: 1
%e A372515   15:
%e A372515   16: 1 2 3 4
%t A372515 Table[Join@@Position[Reverse[IntegerDigits[n,2]],0],{n,30}]
%Y A372515 Row lengths are A023416, partial sums A059015.
%Y A372515 For ones instead of zeros we have A048793, lengths A000120, sums A029931.
%Y A372515 Row sums are A359400, non-reversed A359359.
%Y A372515 Same as A368494 but with empty rows () instead of (0).
%Y A372515 A003714 lists numbers with no successive binary indices.
%Y A372515 A030190 gives binary expansion, reverse A030308.
%Y A372515 A039004 lists the positions of zeros in A345927.
%Y A372515 Cf. A069010, A070939, A073642, A230877, A344618, A359402, A359495.
%K A372515 nonn,base,tabf
%O A372515 1,3
%A A372515 _Gus Wiseman_, May 26 2024