%I #24 Feb 13 2022 06:36:35

%S 0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,20,21,24,25,26,28,29,30,

%T 31,32,33,34,36,37,40,41,42,48,49,50,52,53,56,57,58,60,61,62,63,64,65,

%U 66,68,69,72,73,74,80,81,82,84,85,96,97,98,100,101,104,105

%N Numbers whose binary expansion does not contain 011.

%H Charles R Greathouse IV, <a href="/A004744/b004744.txt">Table of n, a(n) for n = 1..10000</a>

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

%F Sum_{n>=2} 1/a(n) = 6.084750966700965350831194838591995529232464122788387705746226526437263331240... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022

%t Select[Range[0,110],!MemberQ[Partition[IntegerDigits[#,2],3,1],{0,1,1}]&] (* _Harvey P. Dale_, Oct 15 2013 *)

%o (PARI) is(n)=n=binary(n);for(i=3,#n,if(n[i]&&n[i-1]&&!n[i-2], return(0)));1 \\ _Charles R Greathouse IV_, Mar 26 2013

%o (PARI) is(n)=while(n>10, if(bitand(n,7)==3, return(0)); n>>=1); 1 \\ _Charles R Greathouse IV_, Feb 11 2017

%o (Haskell)

%o a004744 n = a004744_list !! (n-1)

%o a004744_list = filter f [0..] where

%o f x = x < 4 || x `mod` 8 /= 3 && f (x `div` 2)

%o -- _Reinhard Zumkeller_, Jul 01 2013

%Y Cf. A007088; A003796 (no 000), A004745 (no 001), A004746 (no 010), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).

%K nonn,base,easy

%O 1,3

%A _N. J. A. Sloane_