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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
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.
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.
Sequence in context: A235873 A118743 A225226 * A114980 A376532 A024372
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 31 2020
STATUS
approved