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%I A346705 #9 Aug 23 2021 10:24:55
%S A346705 0,0,0,1,0,1,2,1,0,1,2,1,4,2,1,3,0,1,2,1,4,2,1,3,8,4,2,5,1,3,6,3,0,1,
%T A346705 2,1,4,2,1,3,8,4,2,5,1,3,6,3,16,8,4,9,2,5,10,5,1,3,6,3,12,6,3,7,0,1,2,
%U A346705 1,4,2,1,3,8,4,2,5,1,3,6,3,16,8,4,9,2,5
%N A346705 The a(n)-th composition in standard order is the even bisection of the n-th composition in standard order.
%C A346705 The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again.
%C A346705 a(n) is the row number in A066099 of the even bisection (even-indexed terms) of the n-th row of A066099.
%F A346705 A029837(a(n)) = A346633(n).
%e A346705 Composition number 741 in standard order is (2,1,1,3,2,1), with even bisection (1,3,1), which is composition number 25 in standard order, so a(741) = 25.
%t A346705 Table[Total[2^Accumulate[Reverse[Last/@Partition[ Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse,2]]]]/2,{n,0,100}]
%Y A346705 Length of the a(n)-th standard composition is A000120(n)/2 rounded down.
%Y A346705 Positions of first appearances appear to be A088698, sorted: A277335.
%Y A346705 The version for reversed prime indices appears to be A329888, sums A346700.
%Y A346705 Sum of the a(n)-th standard composition is A346633.
%Y A346705 An unordered reverse version for odd bisection is A346701, sums A346699.
%Y A346705 The version for odd bisection is A346702, sums A209281(n+1).
%Y A346705 An unordered version for odd bisection is A346703, sums A346697.
%Y A346705 An unordered version is A346704, sums A346698.
%Y A346705 A011782 counts compositions.
%Y A346705 A029837 gives length of binary expansion, or sometimes A070939.
%Y A346705 A066099 lists compositions in standard order.
%Y A346705 A097805 counts compositions by alternating sum.
%Y A346705 Cf. A000302, A025047, A088218, A124754, A124767, A228351, A290258, A290259, A344618, A345197.
%K A346705 nonn
%O A346705 0,7
%A A346705 _Gus Wiseman_, Aug 19 2021

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