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A003796 Numbers with no 3 adjacent 0's in binary expansion. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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.
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).
Sequence in context: A325456 A342524 A328161 * A032896 A032855 A031993
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)