OFFSET
1,3
COMMENTS
First differs from A333223 in lacking 41.
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.
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 02 2020
STATUS
approved