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A004743 Numbers whose binary expansion does not contain 110.

%I A004743 #24 Mar 14 2025 17:56:38
%S A004743 0,1,2,3,4,5,7,8,9,10,11,15,16,17,18,19,20,21,23,31,32,33,34,35,36,37,
%T A004743 39,40,41,42,43,47,63,64,65,66,67,68,69,71,72,73,74,75,79,80,81,82,83,
%U A004743 84,85,87,95,127,128,129,130,131,132,133,135,136,137,138,139
%N A004743 Numbers whose binary expansion does not contain 110.
%H A004743 Charles R Greathouse IV, <a href="/A004743/b004743.txt">Table of n, a(n) for n = 1..10000</a>
%H A004743 Robert Baillie and Thomas Schmelzer, <a href="https://library.wolfram.com/infocenter/MathSource/7166/">Summing Kempner's Curious (Slowly-Convergent) Series</a>, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
%H A004743 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A004743 Sum_{n>=2} 1/a(n) = 5.126608057149204485684180689064467269298250594297584060475240185531109866051... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022
%t A004743 Select[Range[0, 140], !StringContainsQ[IntegerString[#, 2], "110"] &] (* _Amiram Eldar_, Feb 13 2022 *)
%t A004743 Select[Range[0,150],SequenceCount[IntegerDigits[#,2],{1,1,0}]==0&] (* _Harvey P. Dale_, Mar 14 2025 *)
%o A004743 (PARI) is(n)=n=binary(n);for(i=3,#n,if(!n[i]&&n[i-2]&&n[i-1],return(0))); 1 \\ _Charles R Greathouse IV_, Mar 26 2013
%o A004743 (PARI) is(n)=while(n>5, if(bitand(n,7)==6, return(0)); n>>=1); 1 \\ _Charles R Greathouse IV_, Feb 11 2017
%o A004743 (Haskell)
%o A004743 a004743 n = a004743_list !! (n-1)
%o A004743 a004743_list = filter f [0..] where
%o A004743    f x  = x < 4 || x `mod` 8 /= 6 && f (x `div` 2)
%o A004743 -- _Reinhard Zumkeller_, Jul 01 2013
%Y A004743 Cf. A007088; A003796 (no 000), A004745 (no 001), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A003726 (no 111).
%K A004743 nonn,base,easy
%O A004743 1,3
%A A004743 _N. J. A. Sloane_