

A334967


Numbers k such that the every subsequence (not necessarily contiguous) of the kth composition in standard order (A066099) has a different sum.


6



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 15, 16, 17, 18, 19, 20, 21, 24, 26, 28, 31, 32, 33, 34, 35, 36, 40, 42, 48, 56, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 80, 81, 84, 85, 88, 96, 98, 100, 104, 106, 112, 120, 127, 128, 129, 130, 131, 132, 133, 134
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OFFSET

1,3


COMMENTS

First differs from A333223 in lacking 41.
The kth composition in standard order (graded reverselexicographic, 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..64.


EXAMPLE

The sequence together with the corresponding compositions begins:
0: () 18: (3,2) 48: (1,5)
1: (1) 19: (3,1,1) 56: (1,1,4)
2: (2) 20: (2,3) 63: (1,1,1,1,1,1)
3: (1,1) 21: (2,2,1) 64: (7)
4: (3) 24: (1,4) 65: (6,1)
5: (2,1) 26: (1,2,2) 66: (5,2)
6: (1,2) 28: (1,1,3) 67: (5,1,1)
7: (1,1,1) 31: (1,1,1,1,1) 68: (4,3)
8: (4) 32: (6) 69: (4,2,1)
9: (3,1) 33: (5,1) 70: (4,1,2)
10: (2,2) 34: (4,2) 71: (4,1,1,1)
12: (1,3) 35: (4,1,1) 72: (3,4)
15: (1,1,1,1) 36: (3,3) 73: (3,3,1)
16: (5) 40: (2,4) 74: (3,2,2)
17: (4,1) 42: (2,2,2) 80: (2,5)


MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], UnsameQ@@Total/@Union[Subsets[stc[#]]]&]


CROSSREFS

These compositions are counted by A334268.
Golomb rulers are counted by A169942 and ranked by A333222.
Positive subsetsums of partitions are counted by A276024 and A299701.
Knapsack partitions are counted by A108917 and ranked by A299702
Knapsack compositions are counted by A325676 and ranked by A333223.
The case of partitions is counted by A325769 and ranked by A325778.
Contiguous subsequencesums are counted by A333224 and ranked by A333257.
Number of (not necessarily contiguous) subsequences is A334299.
Cf. A000120, A029931, A048793, A066099, A070939, A108917, A124771, A325770, A334300, A334967.
Sequence in context: A281943 A120003 A333223 * A036965 A133184 A102576
Adjacent sequences: A334964 A334965 A334966 * A334968 A334969 A334970


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jun 02 2020


STATUS

approved



