%I #18 Aug 05 2023 08:32:16

%S 965201,653687,429409,272563,166693,98321,56597,32969,20873,15443,

%T 13241,12007,10429,7933,4493,461,-3583,-6961,-9007,-9157,-7019,-2423,

%U 4549,13553,23993,35051,45737,54959,61613,64693,63421,57397,46769,32423,16193,1091,-8443,-6271,15733,67993,163561,318467

%N a(n) = (n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36.

%C Prime generating polynomial found by Jaroslaw Wroblewski and Jean-Charles Meyrignac. The first 55 absolute values (n=0..54) are primes.

%H G. C. Greubel, <a href="/A121888/b121888.txt">Table of n, a(n) for n = 0..1000</a>

%H Ed Pegg Jr., <a href="https://web.archive.org/web/20060812044401/https://www.maa.org/editorial/mathgames/mathgames_07_17_06.html">Math Games, Prime generating polynomials</a>, MAA Online, July 17, 2006

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F From _G. C. Greubel_, Oct 07 2019: (Start)

%F G.f.: (965201 - 6102720*x + 16122821*x^2 - 22787908*x^3 + 18179331*x^4 - 7764198*x^5 + 1387493*x^6)/(1-x)^7.

%F E.g.f.: (34747236 - 11214504*x + 1570248*x^2 - 118824*x^3 + 5022*x^4 -

%F 111*x^5 + x^6)*exp(x)/36. (End)

%p seq((n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36, n=0..30); # _G. C. Greubel_, Oct 07 2019

%t Table[(n^6 -126n^5 +6217n^4 -153066n^3 +1987786n^2 -13055316n +34747236)/36, {n,0,30}] (* modified by _G. C. Greubel_, Oct 07 2019 *)

%o (PARI) vector(30, n, my(m=n-1); (m^6 - 126*m^5 + 6217*m^4 - 153066*m^3 + 1987786*m^2 - 13055316*m + 34747236)/36) \\ _G. C. Greubel_, Oct 07 2019

%o (Magma) [(n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36: n in [0..30]]; // _G. C. Greubel_, Oct 07 2019

%o (Sage) [(n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36 for n in (0..30)] # _G. C. Greubel_, Oct 07 2019

%o (GAP) List([0..30], n-> (n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36); # _G. C. Greubel_, Oct 07 2019

%K sign

%O 0,1

%A _Roger L. Bagula_, Aug 31 2006

%E Edited by _N. J. A. Sloane_, Sep 05 2006

%E Offset corrected by _G. C. Greubel_, Oct 07 2019