

A211775


a(n) = 2*n^2  212*n + 5419.


2



5419, 5209, 5003, 4801, 4603, 4409, 4219, 4033, 3851, 3673, 3499, 3329, 3163, 3001, 2843, 2689, 2539, 2393, 2251, 2113, 1979, 1849, 1723, 1601, 1483, 1369, 1259, 1153, 1051, 953, 859, 769, 683, 601, 523, 449, 379, 313, 251, 193, 139, 89, 43, 1, 37, 71, 101
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OFFSET

0,1


COMMENTS

A "primegenerating" polynomial: This polynomial generates 92 primes (57 being distinct) for n from 0 to 99 (in fact the next seven terms are still primes but we keep the range 099, customary for comparisons), just three primes fewer than the record held by Euler's polynomial for n = m35, which is m^2  69*m + 1231 (see the link below).
The nonprime terms in the first 100 are 1, 1369 = 37^2, 1849 = 43^2, 4033 = 37*109 (all taken twice).
Setting n = 2*m+54 we obtain the polynomial 8*m^2 + 8*m  197, which generates 31 primes in a row starting from m = 0 (the polynomial 8*m^2  488*m + 7243 generates the same 31 primes, but in reverse order).
From Charles Kusniec, Nov 11 2016: The substitution n = m+53 converts this polynomial to the simpler form 2*m^2199.


REFERENCES

Joe L. Mott and Kermite Rose, PrimeProducing Cubic Polynomials in Lecture Notes in Pure and Applied Mathematics (Vol. 220), Marcel Dekker Inc., 2001, pages 281317.


LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000
Joe L. Mott and Kermite Rose, PrimeProducing Cubic Polynomials
E. W. Weisstein, MathWorld: PrimeGenerating Polynomial
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: (541911048*x+5633*x^2)/(1x)^3.  Bruno Berselli, May 18 2012


MAPLE

A211775:=n>2*n^2  212*n + 5419: seq(A211775(n), n=0..100); # Wesley Ivan Hurt, Jan 20 2017


MATHEMATICA

Table[2*n^2  212*n + 5419, {n, 0, 80}] (* Wesley Ivan Hurt, Aug 06 2017 *)


PROG

(MAGMA) [2*n^2212*n+5419: n in [0..49]]; // Bruno Berselli, May 18 2012
(PARI) Vec((541911048*x+5633*x^2)/(1x)^3+O(x^99)) \\ Charles R Greathouse IV, Oct 01 2012
(PARI) a(n) = 2*n^2  212*n + 5419 \\ Charles R Greathouse IV, Dec 19 2016


CROSSREFS

Sequence in context: A203711 A105654 A124410 * A346177 A116894 A124629
Adjacent sequences: A211772 A211773 A211774 * A211776 A211777 A211778


KEYWORD

sign,easy


AUTHOR

Marius Coman, May 18 2012


EXTENSIONS

Edited by N. J. A. Sloane, Nov 12 2016


STATUS

approved



