OFFSET
0,1
COMMENTS
Prime generating polynomial found by Shyam Sunder Gupta. The first 57 values (n=0..56) are primes.
In fact, this polynomial was first found by F. Dress and B. Landreau in 2002 and not by Gupta. See, e.g., Ribenboim's book, page 148. - Hugo Pfoertner, Dec 12 2019
REFERENCES
Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Ed Pegg Jr., Prime generating polynomial, July 17, 2006.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: (-1705829 + 8921273*x - 18696356*x^2 + 19628654*x^3 - 10324925*x^4 + 2177213*x^5)/(1-x)^6. - R. J. Mathar, Sep 13 2011
E.g.f.: (-6823316 + 1568512 x - 139108 x^2 + 5956 x^3 - 123 x^4 + x^5)*exp(x)/4. - G. C. Greubel, Oct 07 2019
MAPLE
seq((n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4, n=0..35); # G. C. Greubel, Oct 07 2019
MATHEMATICA
Table[(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4, {n, 0, 35}]
PROG
(PARI) vector(35, n, my(m=n-1); (m^5 -133*m^4 +6729*m^3 -158379*m^2 +1720294*m -6823316)/4) \\ G. C. Greubel, Oct 07 2019
(Magma) [(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4: n in [0..35]]; // G. C. Greubel, Oct 07 2019
(Sage) [(n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4 for n in (0..35)] # G. C. Greubel, Oct 07 2019
(GAP) List([0..35], n-> (n^5 -133*n^4 +6729*n^3 -158379*n^2 +1720294*n -6823316)/4); # G. C. Greubel, Oct 07 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Aug 31 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 05 2006
STATUS
approved