A121888 a(n) = (n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36.

965201, 653687, 429409, 272563, 166693, 98321, 56597, 32969, 20873, 15443, 13241, 12007, 10429, 7933, 4493, 461, -3583, -6961, -9007, -9157, -7019, -2423, 4549, 13553, 23993, 35051, 45737, 54959, 61613, 64693, 63421, 57397, 46769, 32423, 16193, 1091, -8443, -6271, 15733, 67993, 163561, 318467

Offset

0,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ed Pegg Jr., Math Games, Prime generating polynomials, MAA Online, July 17, 2006

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From G. C. Greubel, Oct 07 2019: (Start)

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

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

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

Maple

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

Mathematica

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Sequence in context: A083609 A093216 A272555 * A178292 A237337 A230030

Adjacent sequences: A121885 A121886 A121887 * A121889 A121890 A121891

Keyword

sign

Author

Roger L. Bagula, Aug 31 2006

Extensions

Edited by N. J. A. Sloane, Sep 05 2006

Offset corrected by G. C. Greubel, Oct 07 2019

Status

approved