A004746 Numbers whose binary expansion does not contain 010.

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

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.

Index entries for 2-automatic sequences.

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

Adjacent sequences: A004743 A004744 A004745 * A004747 A004748 A004749

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved