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A004746 Numbers whose binary expansion does not contain 010.

%I A004746 #23 Feb 13 2022 06:36:04
%S A004746 0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,19,22,23,24,25,27,28,29,30,
%T A004746 31,32,33,35,38,39,44,45,46,47,48,49,51,54,55,56,57,59,60,61,62,63,64,
%U A004746 65,67,70,71,76,77,78,79,88,89,91,92,93,94,95,96,97,99,102
%N A004746 Numbers whose binary expansion does not contain 010.
%H A004746 Reinhard Zumkeller, <a href="/A004746/b004746.txt">Table of n, a(n) for n = 1..10000</a>
%H A004746 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 A004746 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A004746 Sum_{n>=2} 1/a(n) = 7.338340181978485860731253930056466995425939377143636935044890325770833657631... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022
%t A004746 Select[Range[0,110],SequenceCount[IntegerDigits[#,2],{0,1,0}]==0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 19 2015 *)
%o A004746 (PARI) is(n)=n=binary(n);for(i=4,#n,if(!n[i]&&n[i-1]&&!n[i-2], return(0))); 1 \\ _Charles R Greathouse IV_, Mar 29 2013
%o A004746 (PARI) is(n)=while(n>9, if(bitand(n,7)==2, return(0)); n>>=1); 1 \\ _Charles R Greathouse IV_, Feb 11 2017
%o A004746 (Haskell)
%o A004746 a004746 n = a004746_list !! (n-1)
%o A004746 a004746_list = filter f [0..] where
%o A004746    f x  = x < 4 || x `mod` 8 /= 2 && f (x `div` 2)
%o A004746 -- _Reinhard Zumkeller_, Jul 01 2013
%Y A004746 Cf. A007088; A003796 (no 000), A004745 (no 001), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).
%K A004746 nonn,base,easy
%O A004746 1,3
%A A004746 _N. J. A. Sloane_