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A328668
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Numbers whose binary expansion, without the most significant digit, is a necklace.
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6
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0, 1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 16, 17, 19, 21, 23, 31, 32, 33, 35, 37, 39, 43, 47, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 85, 87, 91, 95, 127, 128, 129, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 155, 157, 159, 171, 175, 183, 191, 255, 256, 257
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OFFSET
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0,3
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COMMENTS
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Offset is 0 to be consistent with A257250.
A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
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LINKS
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EXAMPLE
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The sequence of terms together with their binary expansions and binary indices begins:
0: 0 ~ {}
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
4: 100 ~ {3}
5: 101 ~ {1,3}
7: 111 ~ {1,2,3}
8: 1000 ~ {4}
9: 1001 ~ {1,4}
11: 1011 ~ {1,2,4}
15: 1111 ~ {1,2,3,4}
16: 10000 ~ {5}
17: 10001 ~ {1,5}
19: 10011 ~ {1,2,5}
21: 10101 ~ {1,3,5}
23: 10111 ~ {1,2,3,5}
31: 11111 ~ {1,2,3,4,5}
32: 100000 ~ {6}
33: 100001 ~ {1,6}
35: 100011 ~ {1,2,6}
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MATHEMATICA
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neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[0, 100], #<=1||neckQ[Rest[IntegerDigits[#, 2]]]&]
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CROSSREFS
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The version involving all digits, taken in reverse, is A328595.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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