OFFSET
1,2
COMMENTS
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.
LINKS
EXAMPLE
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)
MATHEMATICA
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&]
CROSSREFS
See link for sequences related to standard compositions.
The alternating form is A344619.
Positions of zeros in A357623.
The reverse version is A357628.
The version for prime indices is A357632.
The version for Heinz numbers of partitions is A357636.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2022
STATUS
approved