%I #23 Feb 16 2025 08:33:18
%S 86861,64601,44021,25121,7901,-7639,-21499,-33679,-44179,-52999,
%T -60139,-65599,-69379,-71479,-71899,-70639,-67699,-63079,-56779,
%U -48799,-39139,-27799,-14779,-79,16301,34361,54101,75521,98621,123401,149861,178001,207821,239321,272501
%N a(n) = 840*n^2 - 23100*n + 86861.
%C |a(n)| are distinct primes for 0 <= n <= 32.
%C The values of this polynomial are never divisible by a prime less than 79.
%C All terms are congruent to 1 (mod 20).
%H Arkadiusz Wesolowski, <a href="/A216257/b216257.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://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.: (86861 - 195982*x + 110801*x^2)/(1-x)^3.
%F From _Elmo R. Oliveira_, Feb 10 2025: (Start)
%F E.g.f.: exp(x)*(86861 - 22260*x + 840*x^2).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%p seq(840*n^2-23100*n+86861, n=0..34);
%t Table[840*n^2 - 23100*n + 86861, {n, 0, 34}]
%o (Magma) [ 840*n^2-23100*n+86861 : n in [0..34]]
%o (PARI) for(n=0, 34, print1(840*n^2-23100*n+86861, ", "))
%Y Cf. A141881, A141887, A215145.
%K easy,sign,changed
%O 0,1
%A _Arkadiusz Wesolowski_, Mar 15 2013