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A333630
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Least STC-number of a composition whose sequence of run-lengths has STC-number n.
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5
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..58.
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EXAMPLE
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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)
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MATHEMATICA
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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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 31 2020
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STATUS
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approved
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