A004743 Numbers whose binary expansion does not contain 110.

0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 15, 16, 17, 18, 19, 20, 21, 23, 31, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 47, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 79, 80, 81, 82, 83, 84, 85, 87, 95, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139

Offset

1,3

Links

Charles R Greathouse IV, 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) = 5.126608057149204485684180689064467269298250594297584060475240185531109866051... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022

Mathematica

Select[Range[0, 140], !StringContainsQ[IntegerString[#, 2], "110"] &] (* Amiram Eldar, Feb 13 2022 *)

Prog

(PARI) is(n)=n=binary(n); for(i=3, #n, if(!n[i]&&n[i-2]&&n[i-1], return(0))); 1 \\ Charles R Greathouse IV, Mar 26 2013
(PARI) is(n)=while(n>5, if(bitand(n, 7)==6, return(0)); n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017
(Haskell)
a004743 n = a004743_list !! (n-1)
a004743_list = filter f [0..] where
   f x  = x < 4 || x `mod` 8 /= 6 && f (x `div` 2)
-- Reinhard Zumkeller, Jul 01 2013

Crossrefs

Cf. A007088; A003796 (no 000), A004745 (no 001), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A003726 (no 111).

Sequence in context: A023748 A324845 A107686 * A333764 A333943 A334273

Adjacent sequences: A004740 A004741 A004742 * A004744 A004745 A004746

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved