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%I #36 Aug 01 2022 21:19:51
%S 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,
%T 47,49,51,53,55,57,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,
%U 92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,121,123,125
%N Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...
%H Reinhard Zumkeller, <a href="/A049039/b049039.txt">Rows n=1..13 of triangle, flattened</a>
%H Ralf Stephan, <a href="/somedcgf.html">Some divide-and-conquer sequences ...</a>
%H Ralf Stephan, <a href="/A079944/a079944.ps">Table of generating functions</a>
%F a(n) = 2n - 1 - floor(log_2(n)).
%F a(2^n-1) = 2^(n+1) - (n+2) = A000295(n+1), the Eulerian numbers.
%F a(0)=0, a(2n) = a(n) + 2n - 1, a(2n+1) = a(n) + 2n + 1. - _Ralf Stephan_, Oct 11 2003
%p Digits := 100: [seq(2*n-1-floor(evalf(log(n)/log(2))), n=1..100)];
%t 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_ *)
%o (Haskell)
%o a049039 n k = a049039_tabl !! (n-1) !! (k-1)
%o a049039_row n = a049039_tabl !! (n-1)
%o a049039_tabl = f 1 1 [1..] where
%o f k p xs = ys : f (2 * k) (1 - p) (dropWhile (<= last ys) xs) where
%o ys = take k $ filter ((== p) . (`mod` 2)) xs
%o -- _Reinhard Zumkeller_, Jan 18 2012, Jul 08 2011
%o (PARI) a(n) = n<<1 - 1 - logint(n,2); \\ _Kevin Ryde_, Feb 12 2022
%o (Python)
%o def A049039(n): return (n<<1)-n.bit_length() # _Chai Wah Wu_, Aug 01 2022
%Y Cf. A337300 (partial sums), A043529 (first differences).
%Y Cf. A001614, A033292, A030196, A000295, A050487, A050488.
%Y Cf. A160464, A160465 and A160473. - _Johannes W. Meijer_, May 24 2009
%K easy,nonn,nice,tabf
%O 1,2
%A _James A. Sellers_
%E Keyword tabf added by _Reinhard Zumkeller_, Jan 22 2012
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