OFFSET
1,1
COMMENTS
A finite sequence is aperiodic if its cyclic rotations are all different. - Gus Wiseman, Oct 31 2019
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
For example, 204=(1100 1100)_2 and 292=(100 100 100)_2 belong to the sequence, but 30=(11110)_2 cannot be split into repeating periods.
From Gus Wiseman, Oct 31 2019: (Start)
The sequence of terms together with their binary expansions and binary indices begins:
3: 11 ~ {1,2}
7: 111 ~ {1,2,3}
10: 1010 ~ {2,4}
15: 1111 ~ {1,2,3,4}
31: 11111 ~ {1,2,3,4,5}
36: 100100 ~ {3,6}
42: 101010 ~ {2,4,6}
45: 101101 ~ {1,3,4,6}
54: 110110 ~ {2,3,5,6}
63: 111111 ~ {1,2,3,4,5,6}
127: 1111111 ~ {1,2,3,4,5,6,7}
136: 10001000 ~ {4,8}
153: 10011001 ~ {1,4,5,8}
170: 10101010 ~ {2,4,6,8}
187: 10111011 ~ {1,2,4,5,6,8}
204: 11001100 ~ {3,4,7,8}
221: 11011101 ~ {1,3,4,5,7,8}
238: 11101110 ~ {2,3,4,6,7,8}
255: 11111111 ~ {1,2,3,4,5,6,7,8}
292: 100100100 ~ {3,6,9}
(End)
MATHEMATICA
PeriodicQ[n_, base_] := Block[{l = IntegerDigits[n, base]}, MemberQ[ RotateLeft[l, # ] & /@ Most@ Divisors@ Length@l, l]]; Select[ Range@2599, PeriodicQ[ #, 2] &]
PROG
(PARI) is(n)=n=binary(n); fordiv(#n, d, for(i=1, #n/d-1, for(j=1, d, if(n[j]!=n[j+i*d], next(3)))); return(d<#n)) \\ Charles R Greathouse IV, Dec 10 2013
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Jacob A. Siehler, Sep 08 2006
STATUS
approved