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A004746 Numbers whose binary expansion does not contain 010. 8
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35, 38, 39, 44, 45, 46, 47, 48, 49, 51, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 70, 71, 76, 77, 78, 79, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 102 (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.
FORMULA
Sum_{n>=2} 1/a(n) = 7.338340181978485860731253930056466995425939377143636935044890325770833657631... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022
MATHEMATICA
Select[Range[0, 110], SequenceCount[IntegerDigits[#, 2], {0, 1, 0}]==0&] (* The program uses the SequenceCount function from Mathematica version 10 *) (* Harvey P. Dale, Oct 19 2015 *)
PROG
(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
(PARI) is(n)=while(n>9, if(bitand(n, 7)==2, return(0)); n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017
(Haskell)
a004746 n = a004746_list !! (n-1)
a004746_list = filter f [0..] where
f x = x < 4 || x `mod` 8 /= 2 && f (x `div` 2)
-- Reinhard Zumkeller, Jul 01 2013
CROSSREFS
Cf. A007088; A003796 (no 000), A004745 (no 001), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).
Sequence in context: A083114 A129350 A368365 * A188301 A332110 A178160
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified May 29 10:54 EDT 2024. Contains 372938 sequences. (Running on oeis4.)