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A333630 Least STC-number of a composition whose sequence of run-lengths has STC-number n. 5
0, 1, 3, 5, 7, 14, 11, 13, 15, 30, 43, 29, 23, 46, 27, 45, 31, 62, 122, 61, 87, 117, 59, 118, 47, 94, 107, 93, 55, 110, 91, 109, 63, 126, 250, 125, 343, 245, 123, 246, 175, 350, 235, 349, 119, 238, 347, 237, 95, 190, 378, 189, 215, 373, 187, 374, 111, 222, 363 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

All terms belong to A003754.

A composition of n is a finite sequence of positive integers summing to n. The composition with STC-number k (row k of 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=0..58.

EXAMPLE

The sequence together with the corresponding compositions begins:

   0: ()

   1: (1)

   3: (1,1)

   5: (2,1)

   7: (1,1,1)

  14: (1,1,2)

  11: (2,1,1)

  13: (1,2,1)

  15: (1,1,1,1)

  30: (1,1,1,2)

  43: (2,2,1,1)

  29: (1,1,2,1)

  23: (2,1,1,1)

  46: (2,1,1,2)

  27: (1,2,1,1)

  45: (2,1,2,1)

  31: (1,1,1,1,1)

  62: (1,1,1,1,2)

MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;

seq=Table[Total[2^(Accumulate[Reverse[Length/@Split[stc[n]]]])]/2, {n, 0, 1000}];

Table[Position[seq, i][[1, 1]], {i, First[Split[Union[seq], #1+1==#2&]]}]-1

CROSSREFS

Position of first appearance of n in A333627.

All of the following pertain to compositions in standard order (A066099):

- The length is A000120.

- Compositions without terms > 2 are A003754.

- Compositions without ones are ranked by A022340.

- The partial sums from the right are A048793.

- The sum is A070939.

- Adjacent equal pairs are counted by A124762.

- Equal runs are counted by A124767.

- Strict compositions are ranked by A233564.

- The partial sums from the left are A272020.

- Constant compositions are ranked by A272919.

- Normal compositions are ranked by A333217.

- Heinz number is A333219.

- Anti-runs are counted by A333381.

- Adjacent unequal pairs are counted by A333382.

- Runs-resistance is A333628.

- First appearances of run-resistances are A333629.

Cf. A029931, A098504, A114994, A225620, A228351, A238279, A242882, A318928, A329744, A329747, A333489.

Sequence in context: A235873 A118743 A225226 * A114980 A024372 A295717

Adjacent sequences:  A333627 A333628 A333629 * A333631 A333632 A333633

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 31 2020

STATUS

approved

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Last modified August 13 11:30 EDT 2022. Contains 356091 sequences. (Running on oeis4.)