OFFSET
1,3
COMMENTS
Also numbers whose binary indices together with 0 define a Golomb ruler.
The k-th composition in standard order (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.
LINKS
Wikipedia, Golomb ruler
EXAMPLE
The list of terms together with the corresponding compositions begins:
0: () 41: (2,3,1) 130: (6,2) 262: (6,1,2)
1: (1) 48: (1,5) 132: (5,3) 264: (5,4)
2: (2) 50: (1,3,2) 133: (5,2,1) 265: (5,3,1)
4: (3) 64: (7) 134: (5,1,2) 268: (5,1,3)
5: (2,1) 65: (6,1) 144: (3,5) 272: (4,5)
6: (1,2) 66: (5,2) 145: (3,4,1) 274: (4,3,2)
8: (4) 68: (4,3) 160: (2,6) 276: (4,2,3)
9: (3,1) 69: (4,2,1) 161: (2,5,1) 288: (3,6)
12: (1,3) 70: (4,1,2) 176: (2,1,5) 289: (3,5,1)
16: (5) 72: (3,4) 192: (1,7) 290: (3,4,2)
17: (4,1) 80: (2,5) 194: (1,5,2) 296: (3,2,4)
18: (3,2) 81: (2,4,1) 196: (1,4,3) 304: (3,1,5)
20: (2,3) 88: (2,1,4) 208: (1,2,5) 320: (2,7)
24: (1,4) 96: (1,6) 256: (9) 321: (2,6,1)
32: (6) 98: (1,4,2) 257: (8,1) 324: (2,4,3)
33: (5,1) 104: (1,2,4) 258: (7,2) 328: (2,3,4)
34: (4,2) 128: (8) 260: (6,3) 352: (2,1,6)
40: (2,4) 129: (7,1) 261: (6,2,1) 384: (1,8)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 300], UnsameQ@@ReplaceList[stc[#], {___, s__, ___}:>Plus[s]]&]
CROSSREFS
A subset of A233564.
Also a subset of A333223.
The number of distinct nonzero subsequence-sums is A333224.
The number of distinct subsequence-sums is A333257.
Lengths of optimal Golomb rulers are A003022.
Inequivalent optimal Golomb rulers are counted by A036501.
Golomb subsets are counted by A143823.
Heinz numbers of knapsack partitions are A299702.
Knapsack compositions are counted by A325676.
Maximal Golomb rulers are counted by A325683.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2020
STATUS
approved