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A107909 Numbers having no consecutive zeros or no consecutive ones in binary representation. 11

%I #16 Feb 13 2017 01:53:55

%S 0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,18,20,21,22,23,26,27,29,30,

%T 31,32,33,34,36,37,40,41,42,43,45,46,47,53,54,55,58,59,61,62,63,64,65,

%U 66,68,69,72,73,74,80,81,82,84,85,86,87,90,91,93,94,95,106,107,109,110,111

%N Numbers having no consecutive zeros or no consecutive ones in binary representation.

%C Union of A003754 and A003714, complement of A107911;

%C a(A023548(n+2)) = A052940(n+1) for n>0;

%C a(A001924(n)) = A000225(n) = 2^n - 1;

%C a(A000126(n)) = A000079(n) = 2^n for n>0;

%C A107910(n) = a(n+1) - a(n).

%H Ivan Neretin, <a href="/A107909/b107909.txt">Table of n, a(n) for n = 0..10000</a>

%H J. M. Dusel, <a href="http://math.ucr.edu/~jmd/JohnMDusel_balanced_quotients.pdf">Balanced parabolic quotients and branching rules for Demazure crystals</a>, 2014.

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%o (Perl)

%o foreach $n(1..100){$_=sprintf("%b",$n); print "$n\n" if !m/11/||!m/00/}

%o # _Ivan Neretin_, May 01 2016

%Y Cf. A007088, A107907.

%K nonn,base,easy

%O 0,3

%A _Reinhard Zumkeller_, May 28 2005

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Last modified April 25 01:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)