The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A164707 A positive integer n is included if all runs of 1's in binary n are of the same length. 22
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 27, 28, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 48, 51, 54, 56, 60, 62, 63, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85, 96, 99, 102, 108, 112, 119, 120, 124, 126, 127, 128, 129, 130, 132, 133, 136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Clarification: A binary number consists of "runs" completely of 1's alternating with runs completely of 0's. No two or more runs all of the same digit are adjacent. This sequence contains in part positive integers that each contain one run of 1's. For those members of this sequence each with at least two runs of 1's, see A164709. LINKS Ivan Neretin, Table of n, a(n) for n = 1..10000 EXAMPLE From Gus Wiseman, Oct 31 2019: (Start) 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} 5: 101 ~ {1,3} 6: 110 ~ {2,3} 7: 111 ~ {1,2,3} 8: 1000 ~ {4} 9: 1001 ~ {1,4} 10: 1010 ~ {2,4} 12: 1100 ~ {3,4} 14: 1110 ~ {2,3,4} 15: 1111 ~ {1,2,3,4} 16: 10000 ~ {5} 17: 10001 ~ {1,5} 18: 10010 ~ {2,5} 20: 10100 ~ {3,5} 21: 10101 ~ {1,3,5} 24: 11000 ~ {4,5} 27: 11011 ~ {1,2,4,5} (End) MAPLE isA164707 := proc(n) local bdg, arl, lset ; bdg := convert(n, base, 2) ; lset := {} ; arl := -1 ; for p from 1 to nops(bdg) do if op(p, bdg) = 1 then if p = 1 then arl := 1 ; else arl := arl+1 ; end if; else if arl > 0 then lset := lset union {arl} ; end if; arl := 0 ; end if; end do ; if arl > 0 then lset := lset union {arl} ; end if; return (nops(lset) <= 1 ); end proc: for n from 1 to 300 do if isA164707(n) then printf("%d, ", n) ; end if; end do; # R. J. Mathar, Feb 27 2010 MATHEMATICA Select[Range@ 140, SameQ @@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 1 &]] &] (* Michael De Vlieger, Aug 20 2017 *) PROG (Perl) foreach(1..140){ %runs=(); \$runs{\$_}++ foreach split /0+/, sprintf("%b", \$_); print "\$_, " if 1==keys(%runs); } # Ivan Neretin, Nov 09 2015 CROSSREFS Cf. A164708, A164709, A164710. The version for prime indices is A072774. The binary expansion of n has A069010(n) runs of 1's. Numbers whose runs are all of different lengths are A328592. Partitions with equal multiplicities are A047966. Numbers whose binary expansion is aperiodic are A328594. Numbers whose reversed binary expansion is a necklace are A328595. Numbers whose reversed binary expansion is a Lyndon word are A328596. Cf. A000120, A003714, A014081, A065609, A070939, A121016, A245563, A275692. Sequence in context: A045779 A235028 A062014 * A057890 A161604 A125121 Adjacent sequences: A164704 A164705 A164706 * A164708 A164709 A164710 KEYWORD base,nonn AUTHOR Leroy Quet, Aug 23 2009 EXTENSIONS Extended beyond 42 by R. J. Mathar, Feb 27 2010 STATUS approved

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

Last modified February 29 06:26 EST 2024. Contains 370414 sequences. (Running on oeis4.)