cp's OEIS Frontend

A358333 By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135.

%I A358333 #7 Nov 11 2022 08:08:22
%S A358333 0,1,1,2,2,2,2,3,1,3,2,3,3,3,3,4,2,2,3,4,3,3,3,4,2,4,3,4,4,4,4,5,2,3,
%T A358333 2,3,4,4,4,5,2,4,3,4,4,4,4,5,3,3,4,5,4,4,4,5,3,5,4,5,5,5,5,6,3,3,3,4,
%U A358333 3,3,3,4,3,5,4,5,5,5,5,6,3,3,4,5,4,4,4
%N A358333 By concatenating the standard compositions for each part of the n-th standard composition, we get a sequence of length a(n). Row-lengths of A357135.
%C A358333 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 A358333 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 A358333 Sum of A000120 over row n of A066099.
%e A358333 Composition 92 in standard order is (2,1,1,3), with compositions ((2),(1),(1),(1,1)) so a(92) = 5.
%t A358333 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A358333 Length/@Table[Join@@stc/@stc[n],{n,0,100}]
%Y A358333 See link for sequences related to standard compositions (A066099).
%Y A358333 Dominates A000120.
%Y A358333 Row-lengths of A357135, which is ranked by A357134.
%Y A358333 A related sequence is A358330.
%Y A358333 Cf. A001511, A029931, A048896, A058891, A070939, A096111, A333766, A357137, A357139, A357186, A357187.
%K A358333 nonn
%O A358333 0,4
%A A358333 _Gus Wiseman_, Nov 10 2022