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%I #24 Sep 08 2022 08:46:05
%S 1447,1373,1163,1097,911,853,691,641,503,461,347,313,223,197,131,113,
%T 71,61,43,41,47,53,83,97,151,173,251,281,383,421,547,593,743,797,971,
%U 1033,1231,1301,1523,1601,1847,1933,2203,2297,2591,2693,3011,3121,3463,3581,3947
%N a(n) = ((-1)^n + 2*n - 38)*(2*n - 38) + 41.
%C a(n) are distinct primes for n = 0 to 59.
%C All terms are in A202018.
%H Arkadiusz Wesolowski, <a href="/A226097/b226097.txt">Table of n, a(n) for n = 0..1000</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_782.htm">Puzzle 782</a>
%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_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F G.f.: (1447-2*x*(37+1552*x-41*x^2)+(41*x^2)^2)/((1+x)^2*(1-x)^3).
%F From _Colin Barker_, Aug 14 2017: (Start)
%F G.f.: (1447 - 74*x - 3104*x^2 + 82*x^3 + 1681*x^4) / ((1 - x)^3*(1 + x)^2).
%F a(n) = 4*n^2 - 150*n + 1447 for n even.
%F a(n) = 4*n^2 - 154*n + 1523 for n odd.
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
%F (End)
%t g[n_] := 2*n - 38; f[n_] := ((-1)^n + g[n])*g[n] + 41; Table[f[n], {n, 0, 50}]
%t EulerP[n_] := n^2 - n + 41; f[n_] := 2*n - (3 + (-1)^n)/2; LinearRecurrence[{1, 2, -2, -1, 1}, Table[EulerP@f[n], {n, 19, 15, -1}], {0, 50}]
%o (Magma) [((-1)^n+a)*a+41 where a is 2*n-38 : n in [0..50]]
%o (PARI) Vec((1447 - 74*x - 3104*x^2 + 82*x^3 + 1681*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^100)) \\ _Colin Barker_, Aug 14 2017
%Y Cf. A000040, A005846, A060566, A202018.
%K nonn,easy
%O 0,1
%A _Arkadiusz Wesolowski_, May 26 2013
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