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

3, 10, 11, 13, 14, 36, 37, 38, 39, 41, 44, 50, 51, 52, 57, 60, 136, 137, 138, 139, 140, 141, 142, 143, 145, 152, 162, 163, 168, 177, 184, 196, 197, 198, 199, 200, 209, 216, 226, 227, 232, 241, 248, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..55.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

Example

The terms and corresponding compositions begin:
    3: (1,1)
   10: (2,2)
   11: (2,1,1)
   13: (1,2,1)
   14: (1,1,2)
   36: (3,3)
   37: (3,2,1)
   38: (3,1,2)
   39: (3,1,1,1)
   41: (2,3,1)
   44: (2,1,3)
   50: (1,3,2)
   51: (1,3,1,1)

Mathematica

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 1000], Max@@stc[#]==Total[stc[#]]/2&]

Crossrefs

See link for sequences related to standard compositions.

A066311 lists gapless numbers.

A124767 counts runs in standard compositions.

A333766 gives maximal part of standard compositions, minimal A333768.

A356844 ranks compositions with at least one 1.

Cf. A000120, A001511, A003754, A029931, A329395.

Sequence in context: A114134 A167519 A372120 * A169939 A357627 A073108

Adjacent sequences: A357705 A357706 A357707 * A357709 A357710 A357711

Keyword

nonn

Author

Gus Wiseman, Oct 14 2022

Status

approved