OFFSET
1,2
COMMENTS
The k-th composition in standard order (row k of 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.
EXAMPLE
The sequence together with the corresponding compositions begins:
1: (1)
2: (2)
4: (3)
8: (4)
16: (5)
18: (3,2)
64: (7)
128: (8)
256: (9)
66: (5,2)
1024: (11)
68: (4,3)
4096: (13)
258: (7,2)
132: (5,3)
32768: (16)
65536: (17)
1026: (9,2)
262144: (19)
264: (5,4)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
q=Table[LCM@@stc[n], {n, 10000}];
Table[Position[q, i][[1, 1]], {i, First[Split[Union[q], #1+1==#2&]]}]
CROSSREFS
The version for binary indices is A333492.
The version for prime indices is A330225.
Let q(k) be the k-th composition in standard order:
- The terms of q(k) are row k of A066099.
- The sum of q(k) is A070939(k).
- The product of q(k) is A124758(k).
- The GCD of q(k) is A326674(k).
- The LCM of q(k) is A333226(k).
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 26 2020
STATUS
approved