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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. 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 STATUS approved

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