

A181973


Primegenerating polynomial: 16*n^2  300*n + 1447.


3



1447, 1163, 911, 691, 503, 347, 223, 131, 71, 43, 47, 83, 151, 251, 383, 547, 743, 971, 1231, 1523, 1847, 2203, 2591, 3011, 3463, 3947, 4463, 5011, 5591, 6203, 6847, 7523, 8231, 8971, 9743, 10547, 11383, 12251, 13151, 14083, 15047, 16043, 17071, 18131, 19223
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OFFSET

0,1


COMMENTS

This polynomial generates 30 primes in a row starting from n=0.
The polynomial 16*n^2  628*n + 6203 generates the same primes in reverse order.
I found in the same family of primegenerating polynomials (with the discriminant equal to 163*2^p, where p is even), the polynomials 4n^2  152n + 1607, generating 40 primes in row starting from n=0 (20 distinct ones) and 4n^2  140n + 1877, generating 36 primes in row starting from n=0 (18 distinct ones).
The following 5 (10 with their "reversal" polynomials) are the only ones I know from the family of Euler's polynomial n^2 + n + 41 (having their discriminant equal to a multiple of 163) that generate more than 30 distinct primes in a row starting from n=0 (beside the Escott's polynomial n^2  79n + 1601):
(1) 4n^2  154n + 1523 (4n^2  158n + 1601);
(2) 9n^2  231n + 1523 (9n^2  471n + 6203);
(3) 16n^2  292n + 1373 (16n^2  668n + 7013);
(4) 25n^2  365n + 1373 (25n^2  1185n + 14083);
(5) 16n^2  300n + 1447 (16n^2  628n + 6203).
Note: For the first 2 (4 with their reversals), already reported, see the link below to C. Rivera's site.


LINKS

Bruno Berselli, Table of n, a(n) for n = 0..1000
M. Coman, Ten primegenerating quadratic polynomials, Preprint 2015.
Factor Database, Factorizations of 16n^2300n+1447.
C. Rivera, Puzzle 232: Primes and Cubic polynomials
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

G.f.: (14473178*x+1763*x^2)/(1x)^3.  Bruno Berselli, Apr 06 2012


MATHEMATICA

Table[16*n^2  300*n + 1447, {n, 0, 50}] (* T. D. Noe, Apr 04 2012 *)


PROG

(MAGMA) [n^275*n+1447: n in [0..176 by 4]]; // Bruno Berselli, Apr 06 2012
(PARI) a(n)=16*n^2  300*n + 1447 \\ Charles R Greathouse IV, Dec 08 2014


CROSSREFS

Sequence in context: A031626 A031754 A031536 * A226097 A023311 A208486
Adjacent sequences: A181970 A181971 A181972 * A181974 A181975 A181976


KEYWORD

nonn,easy


AUTHOR

Marius Coman, Apr 04 2012


EXTENSIONS

Offset changed from 1 to 0 by Bruno Berselli, Apr 06 2012


STATUS

approved



