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A121888
a(n) = (n^6 - 126*n^5 + 6217*n^4 - 153066*n^3 + 1987786*n^2 - 13055316*n + 34747236)/36.
1
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
Ed Pegg Jr., Math Games, Prime generating polynomials, MAA Online, July 17, 2006
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
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