A267706 - OEIS

%I #55 Feb 16 2025 08:33:29

%S 27277,23371,19739,16381,13297,10487,7951,5689,3701,1987,547,-619,

%T -1511,-2129,-2473,-2543,-2339,-1861,-1109,-83,1217,2791,4639,6761,

%U 9157,11827,14771,17989,21481,25247,29287,33601,38189,43051,48187,53597,59281,65239,71471,77977

%N a(n) = 137*n^2 - 4043*n + 27277.

%C |a(n)| are distinct primes for 0 <= n <= 39.

%C The values of this polynomial are never divisible by a prime less than 59.

%H Arkadiusz Wesolowski, <a href="/A267706/b267706.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.: (27277 - 58460*x + 31457*x^2)/(1-x)^3.

%F From _Elmo R. Oliveira_, Feb 10 2025: (Start)

%F E.g.f.: exp(x)*(27277 - 3906*x + 137*x^2).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

%p seq(137*n^2-4043*n+27277, n=0..39);

%t Table[137*n^2 - 4043*n + 27277, {n, 0, 39}]

%o (Magma) [137*n^2-4043*n+27277: n in [0..39]];

%o (PARI) for(n=0, 39, print1(137*n^2-4043*n+27277, ", "));

%K sign,easy

%O 0,1

%A _Arkadiusz Wesolowski_, Jan 30 2016