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A335279
Positions of first appearances in A124771 = number of distinct contiguous subsequences of compositions in standard order.
2
0, 1, 3, 5, 11, 15, 23, 27, 37, 47, 55, 107, 111, 119, 155, 215, 223, 239, 411, 431, 471, 479, 495, 549, 631, 943, 951, 959, 991, 1647, 1887, 1967, 1983, 2015, 2543, 2935, 3703, 3807, 3935, 3967, 4031, 6639, 6895, 7407, 7871, 7903, 8063, 8127, 10207, 13279
OFFSET
1,3
EXAMPLE
The sequence together with the corresponding compositions begins:
0: () 215: (1,2,2,1,1,1)
1: (1) 223: (1,2,1,1,1,1,1)
3: (1,1) 239: (1,1,2,1,1,1,1)
5: (2,1) 411: (1,3,1,2,1,1)
11: (2,1,1) 431: (1,2,2,1,1,1,1)
15: (1,1,1,1) 471: (1,1,2,2,1,1,1)
23: (2,1,1,1) 479: (1,1,2,1,1,1,1,1)
27: (1,2,1,1) 495: (1,1,1,2,1,1,1,1)
37: (3,2,1) 549: (4,3,2,1)
47: (2,1,1,1,1) 631: (3,1,1,2,1,1,1)
55: (1,2,1,1,1) 943: (1,1,2,2,1,1,1,1)
107: (1,2,2,1,1) 951: (1,1,2,1,2,1,1,1)
111: (1,2,1,1,1,1) 959: (1,1,2,1,1,1,1,1,1)
119: (1,1,2,1,1,1) 991: (1,1,1,2,1,1,1,1,1)
155: (3,1,2,1,1) 1647: (1,3,1,2,1,1,1,1)
The subsequences for n = 0, 1, 3, 5, 11, 15, 23, 27 are the following (0 = empty partition):
0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1
11 2 2 11 2 2 2 2
21 11 111 11 11 3 11
21 1111 21 12 21 21
211 111 21 32 111
211 121 321 211
2111 211 1111
1211 2111
21111
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
seq=Table[Length[Union[ReplaceList[stc[n], {___, s___, ___}:>{s}]]], {n, 0, 1000}];
Table[Position[seq, i][[1, 1]]-1, {i, First/@Gather[seq]}]
CROSSREFS
Positions of first appearances in A124771.
Compositions where every subinterval has a different sum are A333222.
Knapsack compositions are A333223.
Sequence in context: A244520 A034169 A217384 * A136977 A003529 A018667
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 03 2020
STATUS
approved