

A337666


Numbers k such that any two parts of the kth composition in standard order (A066099) have a common divisor > 1.


13



0, 2, 4, 8, 10, 16, 32, 34, 36, 40, 42, 64, 128, 130, 136, 138, 160, 162, 168, 170, 256, 260, 288, 292, 512, 514, 520, 522, 528, 544, 546, 552, 554, 640, 642, 648, 650, 672, 674, 680, 682, 1024, 2048, 2050, 2052, 2056, 2058, 2080, 2082, 2084, 2088, 2090, 2176
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OFFSET

1,2


COMMENTS

Differs from A291165 in having 1090535424, corresponding to the composition (6,10,15).
This is a ranking sequence for pairwise noncoprime compositions.
The kth composition in standard order (graded reverselexicographic, 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: () 138: (4,2,2) 546: (4,4,2)
2: (2) 160: (2,6) 552: (4,2,4)
4: (3) 162: (2,4,2) 554: (4,2,2,2)
8: (4) 168: (2,2,4) 640: (2,8)
10: (2,2) 170: (2,2,2,2) 642: (2,6,2)
16: (5) 256: (9) 648: (2,4,4)
32: (6) 260: (6,3) 650: (2,4,2,2)
34: (4,2) 288: (3,6) 672: (2,2,6)
36: (3,3) 292: (3,3,3) 674: (2,2,4,2)
40: (2,4) 512: (10) 680: (2,2,2,4)
42: (2,2,2) 514: (8,2) 682: (2,2,2,2,2)
64: (7) 520: (6,4) 1024: (11)
128: (8) 522: (6,2,2) 2048: (12)
130: (6,2) 528: (5,5) 2050: (10,2)
136: (4,4) 544: (4,6) 2052: (9,3)


MATHEMATICA

stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
stabQ[u_, Q_]:=And@@Not/@Q@@@Tuples[u, 2];
Select[Range[0, 1000], stabQ[stc[#], CoprimeQ]&]


CROSSREFS

A337604 counts these compositions of length 3.
A337694 is the version for Heinz numbers of partitions.
A051185 and A305843 (covering) count pairwise intersecting setsystems.
A101268 counts pairwise coprime or singleton compositions.
A318717 counts strict pairwise noncoprime partitions.
A327516 counts pairwise coprime partitions.
A335236 ranks compositions neither a singleton nor pairwise coprime.
A337462 counts pairwise coprime compositions.
All of the following pertain to compositions in standard order (A066099):
 A233564 ranks strict compositions.
 A272919 ranks constant compositions.
 A291166 appears to rank relatively prime compositions.
 A326674 is greatest common divisor.
 A333227 ranks coprime (Mathematica definition) compositions.
 A333228 ranks compositions with distinct parts coprime.
 A335235 ranks singleton or coprime compositions.


KEYWORD

nonn


AUTHOR



STATUS

approved



