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a(n) = 512*n + 1.
4

%I #28 Sep 08 2022 08:45:07

%S 1,513,1025,1537,2049,2561,3073,3585,4097,4609,5121,5633,6145,6657,

%T 7169,7681,8193,8705,9217,9729,10241,10753,11265,11777,12289,12801,

%U 13313,13825,14337,14849,15361,15873,16385,16897,17409,17921,18433

%N a(n) = 512*n + 1.

%C First prime is a(15) = 7681, see A076339.

%H Vincenzo Librandi, <a href="/A076338/b076338.txt">Table of n, a(n) for n = 0..10000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: (1+511*x)/(1-x)^2. - _Vincenzo Librandi_, Feb 23 2012

%F a(n) = 2*a(n-1)-a(n-2). - _Vincenzo Librandi_, Feb 23 2012

%t LinearRecurrence[{2, -1}, {1, 513}, 50] (* _Vincenzo Librandi_, Feb 23 2012 *)

%o (Magma) I:=[1, 513]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 23 2012

%o (PARI) for(n=0, 50, print1(512*n+1", ")); \\ _Vincenzo Librandi_, Feb 23 2012

%o (Haskell)

%o a076338 n = (+ 1) . (* 512)

%o a076338_list = [1,513..] -- _Reinhard Zumkeller_, Mar 08 2012

%Y Cf. A076339.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Oct 07 2002