A003796 Numbers with no 3 adjacent 0's in binary expansion.
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, 30, 31, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92
Offset: 1
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.
- David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.
- Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018.
- Index entries for 2-automatic sequences.
Crossrefs
Programs
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Haskell
a003796 n = a003796_list !! (n-1) a003796_list = filter f [0..] where f x = x < 4 || x `mod` 8 /= 0 && f (x `div` 2) -- Reinhard Zumkeller, Jul 01 2013
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Mathematica
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 *) -
PARI
is(n)=while(n>7,if(bitand(n,7)==0,return(0));n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017
Formula
Sum_{n>=2} 1/a(n) = 9.829256652701616366441622119246549956902006567009112470631751387637507184399... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022