|
|
A329367
|
|
Numbers whose binary expansion, without the most significant digit, is not a necklace.
|
|
1
|
|
|
6, 10, 12, 13, 14, 18, 20, 22, 24, 25, 26, 27, 28, 29, 30, 34, 36, 38, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 83, 84, 86, 88, 89, 90, 92, 93, 94, 96, 97, 98, 99, 100, 101, 102
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
|
|
LINKS
|
|
|
EXAMPLE
|
The sequence of terms together with their binary expansions begins:
6: (1,1,0)
10: (1,0,1,0)
12: (1,1,0,0)
13: (1,1,0,1)
14: (1,1,1,0)
18: (1,0,0,1,0)
20: (1,0,1,0,0)
22: (1,0,1,1,0)
24: (1,1,0,0,0)
25: (1,1,0,0,1)
26: (1,1,0,1,0)
27: (1,1,0,1,1)
28: (1,1,1,0,0)
29: (1,1,1,0,1)
30: (1,1,1,1,0)
34: (1,0,0,0,1,0)
36: (1,0,0,1,0,0)
38: (1,0,0,1,1,0)
40: (1,0,1,0,0,0)
41: (1,0,1,0,0,1)
|
|
MATHEMATICA
|
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[2, 100], !neckQ[Rest[IntegerDigits[#, 2]]]&]
|
|
CROSSREFS
|
The version involving all digits is A062289.
Numbers whose binary expansion is a necklace are A275692.
Numbers whose reversed binary expansion is a necklace are A328595.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|