%I #33 Sep 08 2022 08:46:12
%S 1927,1699,1489,1297,1123,967,829,709,607,523,457,409,379,367,373,397,
%T 439,499,577,673,787,919,1069,1237,1423,1627,1849,2089,2347,2623,2917,
%U 3229,3559,3907,4273,4657,5059,5479,5917,6373,6847,7339,7849,8377,8923,9487,10069
%N a(n) = 9*n^2 - 237*n + 1927.
%C Empirical observation. All integers generated by polynomial for 0 < n <= 37 are prime with the exception of a(26) = 43^2 and a(29) = 43*61.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1927 - 4082*x + 2173*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jun 22 2015
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jun 22 2015
%t Table[9 n^2 - 237 n + 1927, {n, 0, 25}] (* _Michael De Vlieger_, Jun 12 2015 *)
%o (PARI) vector(50, n, 9*n^2 - 237*n + 1927) \\ _Michel Marcus_, Jun 21 2015
%o (Magma) [9*n^2-237*n+1927: n in [0..50]]; // _Vincenzo Librandi_, Jun 22 2015
%Y Cf. A202018, A214732, A215814.
%K nonn,easy,less
%O 0,1
%A _Robert Potter_, Jun 12 2015
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