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60516*n^2 - 61008*n + 2481403.
3

%I #66 Sep 08 2022 08:46:03

%S 2481403,2480911,2601451,2843023,3205627,3689263,4293931,5019631,

%T 5866363,6834127,7922923,9132751,10463611,11915503,13488427,15182383,

%U 16997371,18933391,20990443,23168527,25467643,27887791,30428971,33091183,35874427,38778703,41804011

%N 60516*n^2 - 61008*n + 2481403.

%C The formula gives consecutive primes for n from 1 to 20, except n=9.

%C This is the case m=41*6=246 and k=41 of the polynomial m^2*n^2 + (m^2 - 2*m)*n + (m^2*k) - (m-1).

%H Vincenzo Librandi, <a href="/A215814/b215814.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (2481403-4963298*x+2602927*x^2)/(1-x)^3. - _Bruno Berselli_, Aug 28 2012

%p A215814:=n->60516*n^2 - 61008*n + 2481403; seq(A215814(n), n=0..100); # _Wesley Ivan Hurt_, Nov 28 2013

%t Table[60516 n^2 - 61008 n + 2481403, {n, 0, 30}] (* _Vincenzo Librandi_, Aug 29 2012 *)

%o (Magma) [60516*n^2-61008*n+2481403: n in [0..26]]; // _Bruno Berselli_, Aug 28 2012

%o (PARI) a(n)=60516*n^2-61008*n+2481403 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A214732.

%K nonn,easy

%O 0,1

%A _Robert Potter_, Aug 28 2012

%E Offset changed from 1 to 0 and a(0) added from _Vincenzo Librandi_, Aug 29 2012

%E Gf adapted to the offset by _Bruno Berselli_, Aug 29 2012