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A003726 Numbers with no 3 adjacent 1's in binary expansion. 23
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

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

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Last modified August 8 10:26 EDT 2022. Contains 356009 sequences. (Running on oeis4.)