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Numbers with no 3 adjacent 0's in binary expansion.
15

%I #30 Feb 13 2022 06:38:21

%S 0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,18,19,20,21,22,23,25,26,27,28,29,

%T 30,31,36,37,38,39,41,42,43,44,45,46,47,50,51,52,53,54,55,57,58,59,60,

%U 61,62,63,73,74,75,76,77,78,79,82,83,84,85,86,87,89,90,91,92

%N Numbers with no 3 adjacent 0's in binary expansion.

%H Reinhard Zumkeller, <a href="/A003796/b003796.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 David Garth and Adam Gouge, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Garth/garth14.html">Affinely Self-Generating Sets and Morphisms</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.

%H Chai Wah Wu, <a href="https://arxiv.org/abs/1810.02293">Record values in appending and prepending bitstrings to runs of binary digits</a>, arXiv:1810.02293 [math.NT], 2018.

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

%F Sum_{n>=2} 1/a(n) = 9.829256652701616366441622119246549956902006567009112470631751387637507184399... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - _Amiram Eldar_, Feb 13 2022

%t Select[Range[0,100],SequenceCount[IntegerDigits[#,2],{0,0,0}]==0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 12 2015 *)

%o (Haskell)

%o a003796 n = a003796_list !! (n-1)

%o a003796_list = filter f [0..] where

%o f x = x < 4 || x `mod` 8 /= 0 && f (x `div` 2)

%o -- _Reinhard Zumkeller_, Jul 01 2013

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

%Y Complement of A004779.

%Y Cf. A004745 (no 001), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).

%Y Cf. A063037, A007088.

%K nonn,base,easy

%O 1,3

%A _N. J. A. Sloane_