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 sequence together with the corresponding compositions begins:
34: (4,2) 163: (2,4,1,1) 277: (4,2,2,1)
40: (2,4) 168: (2,2,4) 278: (4,2,1,2)
69: (4,2,1) 177: (2,1,4,1) 279: (4,2,1,1,1)
70: (4,1,2) 184: (2,1,1,4) 282: (4,1,2,2)
81: (2,4,1) 197: (1,4,2,1) 283: (4,1,2,1,1)
88: (2,1,4) 198: (1,4,1,2) 285: (4,1,1,2,1)
98: (1,4,2) 209: (1,2,4,1) 286: (4,1,1,1,2)
104: (1,2,4) 216: (1,2,1,4) 288: (3,6)
130: (6,2) 226: (1,1,4,2) 290: (3,4,2)
138: (4,2,2) 232: (1,1,2,4) 296: (3,2,4)
139: (4,2,1,1) 260: (6,3) 321: (2,6,1)
141: (4,1,2,1) 261: (6,2,1) 324: (2,4,3)
142: (4,1,1,2) 262: (6,1,2) 325: (2,4,2,1)
160: (2,6) 274: (4,3,2) 326: (2,4,1,2)
162: (2,4,2) 276: (4,2,3) 327: (2,4,1,1,1)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 100], !(SameQ@@stc[#]||CoprimeQ@@Union[stc[#]])&]
CROSSREFS
A333228 ranks compositions whose distinct parts are pairwise coprime.
A335238 does not consider a singleton coprime unless it is (1).
A337600 counts 3-part partitions in the complement.
A000740 counts relatively prime compositions.
A051424 counts pairwise coprime or singleton partitions.
A101268 counts pairwise coprime or singleton compositions.
A327516 counts pairwise coprime partitions.
A333227 ranks pairwise coprime compositions.
A337461 counts pairwise coprime 3-part compositions.
A337561 counts pairwise coprime strict compositions.
A337665 counts compositions whose distinct parts are pairwise coprime.
A337666 ranks pairwise non-coprime compositions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 22 2020
STATUS
approved