OFFSET
1,1
COMMENTS
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 terms and their corresponding standard compositions begin:
9: (3,1)
12: (1,3)
17: (4,1)
19: (3,1,1)
24: (1,4)
25: (1,3,1)
28: (1,1,3)
33: (5,1)
34: (4,2)
35: (4,1,1)
39: (3,1,1,1)
40: (2,4)
48: (1,5)
49: (1,4,1)
51: (1,3,1,1)
56: (1,1,4)
57: (1,1,3,1)
60: (1,1,1,3)
MATHEMATICA
nogapQ[m_]:=m=={}||Union[m]==Range[Min[m], Max[m]];
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], !nogapQ[stc[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 01 2022
STATUS
approved