OFFSET
1,3
COMMENTS
A composition of n is a finite sequence of positive integers summing to n. 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 of positive terms together with the corresponding compositions begins:
1: (1) 128: (8) 517: (7,2,1)
2: (2) 129: (7,1) 520: (6,4)
4: (3) 130: (6,2) 521: (6,3,1)
5: (2,1) 132: (5,3) 529: (5,4,1)
8: (4) 133: (5,2,1) 530: (5,3,2)
9: (3,1) 137: (4,3,1) 549: (4,3,2,1)
16: (5) 256: (9) 1024: (11)
17: (4,1) 257: (8,1) 1025: (10,1)
18: (3,2) 258: (7,2) 1026: (9,2)
32: (6) 260: (6,3) 1028: (8,3)
33: (5,1) 261: (6,2,1) 1029: (8,2,1)
34: (4,2) 264: (5,4) 1032: (7,4)
37: (3,2,1) 265: (5,3,1) 1033: (7,3,1)
64: (7) 274: (4,3,2) 1040: (6,5)
65: (6,1) 512: (10) 1041: (6,4,1)
66: (5,2) 513: (9,1) 1042: (6,3,2)
68: (4,3) 514: (8,2) 1058: (5,4,2)
69: (4,2,1) 516: (7,3) 1061: (5,3,2,1)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Select[Range[0, 1000], Greater@@stc[#]&]
CROSSREFS
Strictly increasing runs are counted by A124768.
The normal case is A246534.
The weakly decreasing version is A114994.
The weakly increasing version is A225620.
The unequal version is A233564.
The equal version is A272919.
The strictly increasing version is A333255.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 20 2020
STATUS
approved