A004745 Numbers whose binary expansion does not contain 001.

0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 40, 42, 43, 44, 45, 46, 47, 48, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 80, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 104, 106, 107, 108, 109, 110

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) = 5.808784664093998434778841785199192904637860758506854276321167162567685504669... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022

Mathematica

Select[Range[0, 110], ! StringContainsQ[IntegerString[#, 2], "001"] &] (* Amiram Eldar, Feb 13 2022 *)
Select[Range[0, 120], SequenceCount[IntegerDigits[#, 2], {0, 0, 1}]==0&] (* Harvey P. Dale, Jul 05 2024 *)

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>8, if(bitand(n, 7)==1, return(0)); n>>=1); 1 \\ Charles R Greathouse IV, Feb 11 2017
(Haskell)
a004745 n = a004745_list !! (n-1)
a004745_list = filter f [0..] where
   f x  = x < 4 || x `mod` 8 /= 1 && f (x `div` 2)
-- Reinhard Zumkeller, Jul 01 2013

Crossrefs

Cf. A007088; A003796 (no 000), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110), A003726 (no 111).

Sequence in context: A274375 A364542 A343107 * A158037 A332109 A287519

Adjacent sequences: A004742 A004743 A004744 * A004746 A004747 A004748

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved