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

1,3

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.

Formula

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

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 *)

Prog

(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
(PARI) is(n)=while(n>7, if(bitand(n, 7)==0, return(0)); n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017

Crossrefs

Complement of A004779.

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

Cf. A063037, A007088.

Sequence in context: A325456 A342524 A328161 * A032896 A032855 A031993

Adjacent sequences: A003793 A003794 A003795 * A003797 A003798 A003799

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved