The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A121016 Numbers whose binary expansion is properly periodic. 24
 3, 7, 10, 15, 31, 36, 42, 45, 54, 63, 127, 136, 153, 170, 187, 204, 221, 238, 255, 292, 365, 438, 511, 528, 561, 594, 627, 660, 682, 693, 726, 759, 792, 825, 858, 891, 924, 957, 990, 1023, 2047, 2080, 2145, 2184, 2210, 2275, 2340, 2405, 2457, 2470, 2535 (list; graph; refs; listen; history; text; internal format)
 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 A020330 is a subsequence. Numbers whose binary expansion is aperiodic are A328594. Numbers whose reversed binary expansion is Lyndon are A328596. Numbers whose binary indices have equal run-lengths are A164707. Cf. A000120, A003714, A014081, A065609, A069010, A275692, A328595. Sequence in context: A307612 A330160 A281642 * A246701 A151733 A088636 Adjacent sequences:  A121013 A121014 A121015 * A121017 A121018 A121019 KEYWORD base,easy,nonn AUTHOR Jacob A. Siehler, Sep 08 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 21 04:55 EST 2020. Contains 332086 sequences. (Running on oeis4.)