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A328668
Numbers whose binary expansion, without the most significant digit, is a necklace.
6
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
OFFSET
0,3
COMMENTS
Offset is 0 to be consistent with A257250.
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 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}
MATHEMATICA
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[0, 100], #<=1||neckQ[Rest[IntegerDigits[#, 2]]]&]
CROSSREFS
The dual version is A257250.
The version involving all digits, taken in reverse, is A328595.
The reversed version is A328607.
Binary necklaces are A000031.
Necklace compositions are A008965.
Sequence in context: A371812 A153730 A140691 * A316468 A099627 A324841
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 26 2019
STATUS
approved