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A333768 Minimum part of the n-th composition in standard order. a(0) = 0.

%I A333768 #7 Apr 06 2020 22:12:59
%S A333768 0,1,2,1,3,1,1,1,4,1,2,1,1,1,1,1,5,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,6,1,
%T A333768 2,1,3,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,2,1,
%U A333768 3,1,1,1,3,1,2,1,1,1,1,1,2,1,2,1,2,1,1
%N A333768 Minimum part of the n-th composition in standard order. a(0) = 0.
%C A333768 One plus the shortest run of 0's after a 1 in the binary expansion of n > 0.
%C A333768 A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (row k of 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. This gives a bijective correspondence between nonnegative integers and integer compositions.
%F A333768 For n > 0, a(n) = A333767(n) + 1.
%e A333768 The 148th composition in standard order is (3,2,3), so a(148) = 2.
%t A333768 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A333768 Table[If[n==0,0,Min@@stc[n]],{n,0,100}]
%Y A333768 Positions of first appearances (ignoring index 0) are A000079.
%Y A333768 Positions of terms > 1 are A022340.
%Y A333768 The version for prime indices is A055396.
%Y A333768 The  maximum part is given by A333766.
%Y A333768 All of the following pertain to compositions in standard order (A066099):
%Y A333768 - Length is A000120.
%Y A333768 - Compositions without 1's are A022340.
%Y A333768 - Sum is A070939.
%Y A333768 - Product is A124758.
%Y A333768 - Runs are counted by A124767.
%Y A333768 - Strict compositions are A233564.
%Y A333768 - Constant compositions are A272919.
%Y A333768 - Runs-resistance is A333628.
%Y A333768 - Weakly decreasing compositions are A114994.
%Y A333768 - Weakly increasing compositions are A225620.
%Y A333768 - Strictly decreasing compositions are A333255.
%Y A333768 - Strictly increasing compositions are A333256.
%Y A333768 Cf. A029931, A048793, A087117, A228351, A328594, A333217, A333218, A333219, A333632, A333767.
%K A333768 nonn
%O A333768 0,3
%A A333768 _Gus Wiseman_, Apr 06 2020