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A333222
Numbers k such that every restriction of the k-th composition in standard order to a subinterval has a different sum.
23
0, 1, 2, 4, 5, 6, 8, 9, 12, 16, 17, 18, 20, 24, 32, 33, 34, 40, 41, 48, 50, 64, 65, 66, 68, 69, 70, 72, 80, 81, 88, 96, 98, 104, 128, 129, 130, 132, 133, 134, 144, 145, 160, 161, 176, 192, 194, 196, 208, 256, 257, 258, 260, 261, 262, 264, 265, 268, 272, 274
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.
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.
These compositions are counted by A169942 and A325677.
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.
Complete rulers are A103295, with perfect case A103300.
Knapsack partitions are counted by A108917, with strict case A275972.
Distinct subsequences are counted by A124770 and A124771.
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.
Sequence in context: A285035 A374698 A233564 * A030326 A080086 A229133
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2020
STATUS
approved