login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A182255 81n^2 - 2247n + 15383. 0
15383, 13217, 11213, 9371, 7691, 6173, 4817, 3623, 2591, 1721, 1013, 467, 83, -139, -199, -97, 167, 593, 1181, 1931, 2843, 3917, 5153, 6551, 8111, 9833, 11717, 13763, 15971, 18341, 20873, 23567, 26423, 29441, 32621, 35963, 39467, 43133, 46961, 50951, 55103 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The polynomial generates 33 primes/negative values of primes in a row starting from n=0.

The polynomial 81*n^2 - 2937*n + 26423 generates the same primes in reverse order.

Note: we found in the same family of prime-generating polynomials (with the discriminant equal to 64917 = 3^2*7213) the polynomial 27n^2 - 753n + 4649 (with its "reversed polynomial" 27n^2 - 921n + 7253), generating 32 primes in a row and the polynomial 27n^2 - 741n + 4483 (27n^2 - 1095n + 10501), generating 35 primes in a row, if we consider that 1 is prime (which seems to be constructive in the study of prime-generating polynomials, at least).

Note: the polynomial 36n^2 - 810n + 2753, which is the known quadratic polynomial that generates the most distinct primes in a row (45), has the discriminant equal to 259668 = 2^2*3^2*7213.

LINKS

Table of n, a(n) for n=0..40.

E. W. Weisstein, MathWorld: Prime-Generating Polynomial

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

MATHEMATICA

Table[81n^2-2247n+15383, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {15383, 13217, 11213}, 50] (* Harvey P. Dale, Jan 17 2019 *)

PROG

(PARI) a(n)=81*n^2-2247*n+15383 \\ Charles R Greathouse IV, Oct 01 2012

CROSSREFS

Sequence in context: A054834 A232893 A054835 * A054836 A054837 A252990

Adjacent sequences:  A182252 A182253 A182254 * A182256 A182257 A182258

KEYWORD

sign,easy

AUTHOR

Marius Coman, Apr 21 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 5 23:39 EST 2019. Contains 329784 sequences. (Running on oeis4.)