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A357627
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Numbers k such that the k-th composition in standard order has skew-alternating sum 0.
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13
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0, 3, 10, 11, 15, 36, 37, 38, 43, 45, 54, 55, 58, 59, 63, 136, 137, 138, 140, 147, 149, 153, 166, 167, 170, 171, 175, 178, 179, 183, 190, 191, 204, 205, 206, 212, 213, 214, 219, 221, 228, 229, 230, 235, 237, 246, 247, 250, 251, 255, 528, 529, 530, 532, 536
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OFFSET
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1,2
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COMMENTS
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We define the skew-alternating sum of a sequence (A, B, C, D, E, F, G, ...) to be A - B - C + D + E - F - G + ....
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.
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LINKS
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EXAMPLE
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The sequence together with the corresponding compositions begins:
0: ()
3: (1,1)
10: (2,2)
11: (2,1,1)
15: (1,1,1,1)
36: (3,3)
37: (3,2,1)
38: (3,1,2)
43: (2,2,1,1)
45: (2,1,2,1)
54: (1,2,1,2)
55: (1,2,1,1,1)
58: (1,1,2,2)
59: (1,1,2,1,1)
63: (1,1,1,1,1,1)
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MATHEMATICA
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stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
skats[f_]:=Sum[f[[i]]*(-1)^(1+Ceiling[(i+1)/2]), {i, Length[f]}];
Select[Range[0, 100], skats[stc[#]]==0&]
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CROSSREFS
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See link for sequences related to standard compositions.
The version for prime indices is A357632.
The version for Heinz numbers of partitions is A357636.
A124754 gives alternating sum of standard compositions, reverse A344618.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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