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A153234 a(n) = floor(2^n/9). 8

%I

%S 0,0,0,0,1,3,7,14,28,56,113,227,455,910,1820,3640,7281,14563,29127,

%T 58254,116508,233016,466033,932067,1864135,3728270,7456540,14913080,

%U 29826161,59652323,119304647,238609294,477218588,954437176,1908874353,3817748707,7635497415,15270994830

%N a(n) = floor(2^n/9).

%C Partial sums of A113405. - _Mircea Merca_, Dec 28 2010

%C Dubickas proves that infinitely many terms of this sequence are composite. - _Charles R Greathouse IV_, Feb 04 2016

%H Vincenzo Librandi, <a href="/A153234/b153234.txt">Table of n, a(n) for n = 0..1000</a>

%H Artūras Dubickas, <a href="http://dx.doi.org/10.1007/s00605-008-0042-6">Prime and composite integers close to powers of a number</a>, Monatsh. Math. 158:3 (2009), pp. 271-284.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,3,-2).

%F a(n+1) - 2*a(n) = A088911(n+3).

%F a(n) + a(n+3) = 2^n - 1 = A000225(n), n > 0.

%F From _Mircea Merca_, Dec 28 2010: (Start)

%F a(n) = round((2*2^n-9)/18) = floor((2^n-1)/9) = ceiling((2^n-8)/9).

%F a(n) = a(n-6) + 7*2^(n-6), n > 5. (End)

%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 3*a(n-4) - 2*a(n-5).

%F G.f.: x^4 / ( (1-2*x)*(1-x^2)*(1-x+x^2) ).

%F a(n) + a(n+1) = A111927(n). - _R. J. Mathar_, Apr 08 2013

%p seq(floor(2^n/9),n=0..25); # _Mircea Merca_, Dec 28 2010

%t Table[Floor[2^n/9], {n, 0, 37}] (* _Michael De Vlieger_, Mar 26 2016 *)

%o (MAGMA) [Round((2*2^n-9)/18): n in [0..40]]; // _Vincenzo Librandi_, Jun 25 2011

%o (PARI) a(n)=2^n\9 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (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

%o (Sage) [floor(2^n/9) for n in (0..40)] # _G. C. Greubel_, Jun 05 2019

%Y Cf. A113405.

%K nonn,easy

%O 0,6

%A _Paul Curtz_, Dec 21 2008

%E More terms from _Vincenzo Librandi_, Jun 25 2011

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)