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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
OFFSET
1,1
COMMENTS
A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
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 complement is A328668.
The version involving all digits is A062289.
The reverse version is A328607.
Binary necklaces are A000031.
Necklace compositions are A008965.
Numbers whose binary expansion is a necklace are A275692.
Numbers whose reversed binary expansion is a necklace are A328595.
Sequence in context: A141467 A361109 A317719 * A343311 A348718 A325265
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 15 2019
STATUS
approved