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 A153234 a(n) = floor(2^n/9). 8
 0, 0, 0, 0, 1, 3, 7, 14, 28, 56, 113, 227, 455, 910, 1820, 3640, 7281, 14563, 29127, 58254, 116508, 233016, 466033, 932067, 1864135, 3728270, 7456540, 14913080, 29826161, 59652323, 119304647, 238609294, 477218588, 954437176, 1908874353, 3817748707, 7635497415, 15270994830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Partial sums of A113405. - Mircea Merca, Dec 28 2010 Dubickas proves that infinitely many terms of this sequence are composite. - Charles R Greathouse IV, Feb 04 2016 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 ArtÅ«ras Dubickas, Prime and composite integers close to powers of a number, Monatsh. Math. 158:3 (2009), pp. 271-284. Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,3,-2). FORMULA a(n+1) - 2*a(n) = A088911(n+3). a(n) + a(n+3) = 2^n - 1 = A000225(n), n > 0. From Mircea Merca, Dec 28 2010: (Start) a(n) = round((2*2^n-9)/18) = floor((2^n-1)/9) = ceiling((2^n-8)/9). a(n) = a(n-6) + 7*2^(n-6), n > 5. (End) a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 3*a(n-4) - 2*a(n-5). G.f.: x^4 / ( (1-2*x)*(1-x^2)*(1-x+x^2) ). a(n) + a(n+1) = A111927(n). - R. J. Mathar, Apr 08 2013 MAPLE seq(floor(2^n/9), n=0..25); # Mircea Merca, Dec 28 2010 MATHEMATICA Table[Floor[2^n/9], {n, 0, 37}] (* Michael De Vlieger, Mar 26 2016 *) PROG (MAGMA) [Round((2*2^n-9)/18): n in [0..40]]; // Vincenzo Librandi, Jun 25 2011 (PARI) a(n)=2^n\9 \\ Charles R Greathouse IV, Oct 07 2015 (PARI) x='x+O('x^44); concat(vector(4), Vec(x^4/((x-1)*(2*x-1)*(1+x)*(x^2-x+1)))) \\ Altug Alkan, Mar 25 2016 (Sage) [floor(2^n/9) for n in (0..40)] # G. C. Greubel, Jun 05 2019 CROSSREFS Cf. A113405. Sequence in context: A088209 A089074 A125176 * A293334 A266625 A151754 Adjacent sequences:  A153231 A153232 A153233 * A153235 A153236 A153237 KEYWORD nonn,easy AUTHOR Paul Curtz, Dec 21 2008 EXTENSIONS More terms from Vincenzo Librandi, Jun 25 2011 STATUS approved

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Last modified August 9 22:42 EDT 2020. Contains 336335 sequences. (Running on oeis4.)