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Numbers whose binary expansion does not contain 010.
8

%I #23 Feb 13 2022 06:36:04

%S 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 31,32,33,35,38,39,44,45,46,47,48,49,51,54,55,56,57,59,60,61,62,63,64,

%U 65,67,70,71,76,77,78,79,88,89,91,92,93,94,95,96,97,99,102

%N Numbers whose binary expansion does not contain 010.

%H Reinhard Zumkeller, <a href="/A004746/b004746.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) = 7.338340181978485860731253930056466995425939377143636935044890325770833657631... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022

%t 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 (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 (PARI) is(n)=while(n>9, if(bitand(n,7)==2, return(0)); n>>=1); 1 \\ _Charles R Greathouse IV_, Feb 11 2017

%o (Haskell)

%o a004746 n = a004746_list !! (n-1)

%o a004746_list = filter f [0..] where

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

%o -- _Reinhard Zumkeller_, Jul 01 2013

%Y Cf. A007088; A003796 (no 000), A004745 (no 001), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).

%K nonn,base,easy

%O 1,3

%A _N. J. A. Sloane_