OFFSET
1,2
COMMENTS
A necklace is a finite sequence that is lexicographically minimal among all of its cyclic rotations.
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of terms together with their binary expansions and binary indices begins:
1: 1 ~ {1}
2: 10 ~ {2}
3: 11 ~ {1,2}
4: 100 ~ {3}
6: 110 ~ {2,3}
7: 111 ~ {1,2,3}
8: 1000 ~ {4}
10: 1010 ~ {2,4}
12: 1100 ~ {3,4}
14: 1110 ~ {2,3,4}
15: 1111 ~ {1,2,3,4}
16: 10000 ~ {5}
20: 10100 ~ {3,5}
24: 11000 ~ {4,5}
26: 11010 ~ {2,4,5}
28: 11100 ~ {3,4,5}
30: 11110 ~ {2,3,4,5}
31: 11111 ~ {1,2,3,4,5}
32: 100000 ~ {6}
36: 100100 ~ {3,6}
MATHEMATICA
neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And];
Select[Range[100], neckQ[Reverse[IntegerDigits[#, 2]]]&]
PROG
(Python)
from itertools import count, islice
from sympy.utilities.iterables import necklaces
def a_gen():
for n in count(1):
t = []
for i in necklaces(n, 2):
if sum(i)>0:
t.append(sum(2**j for j in range(len(i)) if i[j] > 0))
yield from sorted(t)
A328595_list = list(islice(a_gen(), 100)) # John Tyler Rascoe, May 24 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Oct 22 2019
STATUS
approved