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%I #23 Oct 31 2019 14:33:00
%S 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,
%T 36,37,40,41,42,48,51,54,56,60,62,63,64,65,66,68,69,72,73,74,80,81,82,
%U 84,85,96,99,102,108,112,119,120,124,126,127,128,129,130,132,133,136
%N A positive integer n is included if all runs of 1's in binary n are of the same length.
%C 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.
%C 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.
%H Ivan Neretin, <a href="/A164707/b164707.txt">Table of n, a(n) for n = 1..10000</a>
%e From _Gus Wiseman_, Oct 31 2019: (Start)
%e The sequence of terms together with their binary expansions and binary indices begins:
%e 1: 1 ~ {1}
%e 2: 10 ~ {2}
%e 3: 11 ~ {1,2}
%e 4: 100 ~ {3}
%e 5: 101 ~ {1,3}
%e 6: 110 ~ {2,3}
%e 7: 111 ~ {1,2,3}
%e 8: 1000 ~ {4}
%e 9: 1001 ~ {1,4}
%e 10: 1010 ~ {2,4}
%e 12: 1100 ~ {3,4}
%e 14: 1110 ~ {2,3,4}
%e 15: 1111 ~ {1,2,3,4}
%e 16: 10000 ~ {5}
%e 17: 10001 ~ {1,5}
%e 18: 10010 ~ {2,5}
%e 20: 10100 ~ {3,5}
%e 21: 10101 ~ {1,3,5}
%e 24: 11000 ~ {4,5}
%e 27: 11011 ~ {1,2,4,5}
%e (End)
%p 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
%t Select[Range@ 140, SameQ @@ Map[Length, Select[Split@ IntegerDigits[#, 2], First@ # == 1 &]] &] (* _Michael De Vlieger_, Aug 20 2017 *)
%o (Perl)
%o foreach(1..140){
%o %runs=();
%o $runs{$_}++ foreach split /0+/, sprintf("%b",$_);
%o print "$_, " if 1==keys(%runs);
%o }
%o # _Ivan Neretin_, Nov 09 2015
%Y Cf. A164708, A164709, A164710.
%Y The version for prime indices is A072774.
%Y The binary expansion of n has A069010(n) runs of 1's.
%Y Numbers whose runs are all of different lengths are A328592.
%Y Partitions with equal multiplicities are A047966.
%Y Numbers whose binary expansion is aperiodic are A328594.
%Y Numbers whose reversed binary expansion is a necklace are A328595.
%Y Numbers whose reversed binary expansion is a Lyndon word are A328596.
%Y Cf. A000120, A003714, A014081, A065609, A070939, A121016, A245563, A275692.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Aug 23 2009
%E Extended beyond 42 by _R. J. Mathar_, Feb 27 2010
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