A004744 - OEIS

A004744

Numbers whose binary expansion does not contain 011.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 48, 49, 50, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85, 96, 97, 98, 100, 101, 104, 105

(list; graph; refs; listen; history; text; internal format)

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) = 6.084750966700965350831194838591995529232464122788387705746226526437263331240... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022

MATHEMATICA

Select[Range[0, 110], !MemberQ[Partition[IntegerDigits[#, 2], 3, 1], {0, 1, 1}]&] (* Harvey P. Dale, Oct 15 2013 *)

PROG

(PARI) is(n)=n=binary(n); for(i=3, #n, if(n[i]&&n[i-1]&&!n[i-2], return(0))); 1 \\ Charles R Greathouse IV, Mar 26 2013

(PARI) is(n)=while(n>10, if(bitand(n, 7)==3, return(0)); n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017

(Haskell)

a004744 n = a004744_list !! (n-1)

a004744_list = filter f [0..] where

f x = x < 4 || x `mod` 8 /= 3 && f (x `div` 2)

-- Reinhard Zumkeller, Jul 01 2013

CROSSREFS

Cf. A007088; A003796 (no 000), A004745 (no 001), A004746 (no 010), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).

Sequence in context: A335523 A374519 A328869 * A171987 A332111 A072226

Adjacent sequences: A004741 A004742 A004743 * A004745 A004746 A004747

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane

STATUS

approved