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%I #33 Feb 09 2025 10:26:15
%S 683,499,347,227,139,83,59,67,107,179,283,419,587,787,1019,1283,1579,
%T 1907,2267,2659,3083,3539,4027,4547,5099,5683,6299,6947,7627,8339,
%U 9083,9859,10667,11507,12379,13283,14219,15187,16187,17219,18283,19379,20507,21667,22859,24083,25339,26627,27947
%N Prime generating polynomial: a(n) = (4*n - 29)^2 + 58.
%C The polynomial (4*n - 29)^2 + 58 generates 28 distinct primes in succession from n=1 to 28.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Elmo R. Oliveira_, Feb 08 2025: (Start)
%F G.f.: x*(899*x^2 - 1550*x + 683)/(1-x)^3.
%F E.g.f.: exp(x)*(16*x^2 - 216*x + 899) - 899.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t Array[(4# - 29)^2 + 58 &, 50] (* _Amiram Eldar_, Dec 15 2018 *)
%Y Cf. A048988.
%K nonn,easy,changed
%O 1,1
%A _Arashdeep Singh_, Oct 21 2018