cp's OEIS Frontend

A358138 Difference between maximum and minimum part in the n-th composition in standard order.

%I A358138 #6 Oct 31 2022 22:05:28
%S A358138 0,0,0,0,1,1,0,0,2,0,1,2,1,1,0,0,3,1,2,1,1,1,1,3,2,1,1,2,1,1,0,0,4,2,
%T A358138 3,0,2,2,2,2,2,0,1,2,1,1,1,4,3,2,2,2,1,1,1,3,2,1,1,2,1,1,0,0,5,3,4,1,
%U A358138 3,3,3,1,2,1,2,2,2,2,2,3,3,1,2,1,1,1,1
%N A358138 Difference between maximum and minimum part in the n-th composition in standard order.
%C A358138 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 A358138 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%F A358138 a(n) = A333766(n) - A333768(n).
%t A358138 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A358138 Table[Max[stc[n]]-Min[stc[n]],{n,1,100}]
%Y A358138 See link for sequences related to standard compositions.
%Y A358138 The first and last parts are A065120 and A001511, difference A358135.
%Y A358138 This is the maximum minus minimum part in row n of A066099.
%Y A358138 The version for Heinz numbers of partitions is A243055.
%Y A358138 The maximum and minimum parts are A333766 and A333768.
%Y A358138 The partial sums of standard compositions are A358134, adjusted A242628.
%Y A358138 A011782 counts compositions.
%Y A358138 A351014 counts distinct runs in standard compositions.
%Y A358138 Cf. A000120, A029837, A029931, A048896, A058891, A070939, A133494, A329395, A357187, A358133.
%K A358138 nonn
%O A358138 1,9
%A A358138 _Gus Wiseman_, Oct 31 2022