login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003726 Numbers with no 3 adjacent 1's in binary expansion. 28
0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 80, 81, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Positions of zeros in A014082. Could be called "tribbinary numbers" by analogy with A003714. - John Keith, Mar 07 2022

The sequence of Tribbinary numbers can be constructed by writing out the Tribonacci representations of nonnegative integers and then evaluating the result in binary. These numbers are similar to Fibbinary numbers A003714, Fibternary numbers A003726, and Tribternary numbers A356823. The number of Tribbinary numbers less than any power of two is a Tribonacci number. We can generate Tribbinary numbers recursively: Start by adding 0 and 1 to the sequence. Then, if x is a number in the sequence add 2x, 4x+1, and 8x+3 to the sequence. The n-th Tribbinary number is even if the n-th term of the Tribonacci word is a. Respectively, the n-th Tribbinary number is of the form 4x+1 if the n-th term of the Tribonacci word is b, and the n-th Tribbinary number is of the form 8x+3 if the n-th term of the Tribonacci word is c. Every nonnegative integer can be written as the sum of two Tribbinary numbers. Every number has a Tribbinary multiple. - Tanya Khovanova and PRIMES STEP Senior, Aug 30 2022

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

There are A000073(n+3) terms of this sequence with at most n bits. In particular, a(A000073(n+3)+1) = 2^n. - Charles R Greathouse IV, Oct 22 2021

Sum_{n>=2} 1/a(n) = 9.516857810319139410424631558212354346868048230248717360943194590798113163384... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 13 2022

MATHEMATICA

Select[Range[0, 82], SequenceCount[IntegerDigits[#, 2], {1, 1, 1}] == 0 &] (* Michael De Vlieger, Dec 23 2019 *)

PROG

(Haskell)

a003726 n = a003726_list !! (n - 1)

a003726_list = filter f [0..] where

   f x = x < 7 || (x `mod` 8) < 7 && f (x `div` 2)

-- Reinhard Zumkeller, Jun 03 2012

(PARI) is(n)=!bitand(bitand(n, n<<1), n<<2) \\ Charles R Greathouse IV, Feb 11 2017

CROSSREFS

Cf. A278038 (binary), A063037, A000073, A014082 (number of 111).

Cf. A004781 (complement).

Cf. A007088; A003796 (no 000), A004745 (no 001), A004746 (no 010), A004744 (no 011), A003754 (no 100), A004742 (no 101), A004743 (no 110).

Sequence in context: A325114 A004765 A247063 * A343110 A337582 A004828

Adjacent sequences:  A003723 A003724 A003725 * A003727 A003728 A003729

KEYWORD

nonn,base,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 07:57 EST 2022. Contains 358354 sequences. (Running on oeis4.)