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 A004780 Binary expansion contains 2 adjacent 1's. 13
 3, 6, 7, 11, 12, 13, 14, 15, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 38, 39, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 70, 71, 75, 76, 77, 78, 79, 83, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Complement of A003714. It appears that n is in the sequence if and only if C(3n,n) is even. - Benoit Cloitre, Mar 09 2003 Since the binary representation of these numbers contains two adjacent 1's, so for these values of n, we will have (n XOR 2n XOR 3n) != 0, and thus a two player Nim game with three heaps of (n, 2n, 3n) stones will be a winning configuration for the first player. - V. Raman, Sep 17 2012 A048728(a(n)) > 0. - Reinhard Zumkeller, May 13 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Index entries for sequences related to binary expansion of n FORMULA a(n) ~ n. - Charles R Greathouse IV, Sep 19 2012 MAPLE q:= n-> verify([1\$2], Bits[Split](n), 'sublist'): select(q, [\$0..200])[]; # Alois P. Heinz, Oct 22 2021 PROG (PARI) is(n)=bitand(n, n+n)>0 \\ Charles R Greathouse IV, Sep 19 2012 (Haskell) a004780 n = a004780_list !! (n-1) a004780_list = filter ((> 1) . a048728) [1..] -- Reinhard Zumkeller, May 13 2014 (Python) from itertools import count, islice def A004780_gen(startvalue=1): # generator of terms >= startvalue return filter(lambda n:n&(n<<1), count(max(startvalue, 1))) A004780_list = list(islice(A004780_gen(), 30)) # Chai Wah Wu, Jul 13 2022 CROSSREFS Cf. A005809, A048728, A242408. Complement: A003714. Subsequences (apart from any initial zero-term): A001196, A004755, A004767, A033428, A277335. Sequence in context: A292608 A028754 A028795 * A359266 A292046 A051146 Adjacent sequences: A004777 A004778 A004779 * A004781 A004782 A004783 KEYWORD nonn,easy,base AUTHOR N. J. A. Sloane EXTENSIONS Offset corrected by Reinhard Zumkeller, Jul 28 2010 STATUS approved

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Last modified April 21 14:03 EDT 2024. Contains 371870 sequences. (Running on oeis4.)