A049039 Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...

1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 26, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121, 123, 125

Offset: 1

Author

James Sellers

Keywords

• easy
• nonn
• nice
• tabf

Links

• Reinhard Zumkeller, Rows n=1..13 of triangle, flattened
• Ralf Stephan, Some divide-and-conquer sequences ...
• Ralf Stephan, Table of generating functions

Crossrefs

Cf. A337300 (partial sums), A043529 (first differences).

Cf. A001614, A033292, A030196, A000295, A050487, A050488.

Cf. A160464, A160465 and A160473. - Johannes W. Meijer, May 24 2009

Programs

Haskell

a049039 n k = a049039_tabl !! (n-1) !! (k-1)
a049039_row n = a049039_tabl !! (n-1)
a049039_tabl = f 1 1 [1..] where
   f k p xs = ys : f (2 * k) (1 - p) (dropWhile (<= last ys) xs) where
     ys  = take k $ filter ((== p) . (`mod` 2)) xs
-- Reinhard Zumkeller, Jan 18 2012, Jul 08 2011

Maple

Digits := 100: [seq(2*n-1-floor(evalf(log(n)/log(2))), n=1..100)];

Mathematica

a[0] = 0; a[n_?EvenQ] := a[n] = a[n/2]+n-1; a[n_?OddQ] := a[n] = a[(n-1)/2]+n; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 27 2011, after Ralf Stephan *)

PARI

a(n) = n<<1 - 1 - logint(n,2); \\ Kevin Ryde, Feb 12 2022

Python

def A049039(n): return (n<<1)-n.bit_length() # Chai Wah Wu, Aug 01 2022

Formula

a(n) = 2n - 1 - floor(log_2(n)).

a(2^n-1) = 2^(n+1) - (n+2) = A000295(n+1), the Eulerian numbers.

a(0)=0, a(2n) = a(n) + 2n - 1, a(2n+1) = a(n) + 2n + 1. - Ralf Stephan, Oct 11 2003

Extensions

Keyword tabf added by Reinhard Zumkeller, Jan 22 2012