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A004745 Numbers whose binary expansion does not contain 001.

%I A004745 #24 Jul 05 2024 18:33:01
%S A004745 0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,20,21,22,23,24,26,27,28,29,30,
%T A004745 31,32,40,42,43,44,45,46,47,48,52,53,54,55,56,58,59,60,61,62,63,64,80,
%U A004745 84,85,86,87,88,90,91,92,93,94,95,96,104,106,107,108,109,110
%N A004745 Numbers whose binary expansion does not contain 001.
%H A004745 Reinhard Zumkeller, <a href="/A004745/b004745.txt">Table of n, a(n) for n = 1..10000</a>
%H A004745 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 A004745 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A004745 Sum_{n>=2} 1/a(n) = 5.808784664093998434778841785199192904637860758506854276321167162567685504669... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022
%t A004745 Select[Range[0, 110], ! StringContainsQ[IntegerString[#, 2], "001"] &] (* _Amiram Eldar_, Feb 13 2022 *)
%t A004745 Select[Range[0,120],SequenceCount[IntegerDigits[#,2],{0,0,1}]==0&] (* _Harvey P. Dale_, Jul 05 2024 *)
%o A004745 (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 A004745 (PARI) is(n)=while(n>8, if(bitand(n,7)==1, return(0)); n>>=1); 1 \\ _Charles R Greathouse IV_, Feb 11 2017
%o A004745 (Haskell)
%o A004745 a004745 n = a004745_list !! (n-1)
%o A004745 a004745_list = filter f [0..] where
%o A004745    f x  = x < 4 || x `mod` 8 /= 1 && f (x `div` 2)
%o A004745 -- _Reinhard Zumkeller_, Jul 01 2013
%Y A004745 Cf. A007088; A003796 (no 000), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).
%K A004745 nonn,base,easy
%O A004745 1,3
%A A004745 _N. J. A. Sloane_