cp's OEIS Frontend

A357138 Minimal run-length of the n-th composition in standard order; a(0) = 0.

%I A357138 #6 Sep 24 2022 14:58:24
%S A357138 0,1,1,2,1,1,1,3,1,1,2,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,
%T A357138 1,1,2,1,1,1,1,1,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,6,1,1,1,1,
%U A357138 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A357138 Minimal run-length of the n-th composition in standard order; a(0) = 0.
%C A357138 A composition of n is a finite sequence of positive integers summing to n. 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. This gives a bijective correspondence between nonnegative integers and integer compositions.
%H A357138 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%e A357138 Composition 92 in standard order is (2,1,1,3), so a(92) = 1.
%t A357138 stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A357138 Table[If[n==0,0,Min[Length/@Split[stc[n]]]],{n,0,100}]
%Y A357138 See link for more sequences related to standard compositions.
%Y A357138 The version for Heinz numbers of partitions is A051904, for parts A055396.
%Y A357138 For parts instead of run-length we have A333768, maximal A333766.
%Y A357138 The opposite (maximal) version is A357137.
%Y A357138 For first instead of minimal we have A357180, last A357181.
%Y A357138 Cf. A000120, A001511, A003754, A029931, A051903, A056239, A061395, A070939, A297173, A356844, A357136.
%K A357138 nonn
%O A357138 0,4
%A A357138 _Gus Wiseman_, Sep 18 2022