A004780 Binary expansion contains 2 adjacent 1's.

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

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