cp's OEIS Frontend

A357708 Numbers k such that the k-th composition in standard order has sum equal to twice its maximum part.

%I A357708 #6 Oct 15 2022 08:10:51
%S A357708 3,10,11,13,14,36,37,38,39,41,44,50,51,52,57,60,136,137,138,139,140,
%T A357708 141,142,143,145,152,162,163,168,177,184,196,197,198,199,200,209,216,
%U A357708 226,227,232,241,248,528,529,530,531,532,533,534,535,536,537,538,539
%N A357708 Numbers k such that the k-th composition in standard order has sum equal to twice its maximum part.
%C A357708 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 A357708 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 A357708 The terms and corresponding compositions begin:
%e A357708     3: (1,1)
%e A357708    10: (2,2)
%e A357708    11: (2,1,1)
%e A357708    13: (1,2,1)
%e A357708    14: (1,1,2)
%e A357708    36: (3,3)
%e A357708    37: (3,2,1)
%e A357708    38: (3,1,2)
%e A357708    39: (3,1,1,1)
%e A357708    41: (2,3,1)
%e A357708    44: (2,1,3)
%e A357708    50: (1,3,2)
%e A357708    51: (1,3,1,1)
%t A357708 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A357708 Select[Range[0,1000],Max@@stc[#]==Total[stc[#]]/2&]
%Y A357708 See link for sequences related to standard compositions.
%Y A357708 A066311 lists gapless numbers.
%Y A357708 A124767 counts runs in standard compositions.
%Y A357708 A333766 gives maximal part of standard compositions, minimal A333768.
%Y A357708 A356844 ranks compositions with at least one 1.
%Y A357708 Cf. A000120, A001511, A003754, A029931, A329395.
%K A357708 nonn
%O A357708 1,1
%A A357708 _Gus Wiseman_, Oct 14 2022