|
| |
|
|
A267252
|
|
Primes of the form abs(103*n^2 - 4707*n + 50383) in order of increasing nonnegative n.
|
|
4
|
|
|
|
50383, 45779, 41381, 37189, 33203, 29423, 25849, 22481, 19319, 16363, 13613, 11069, 8731, 6599, 4673, 2953, 1439, 131, 971, 1867, 2557, 3041, 3319, 3391, 3257, 2917, 2371, 1619, 661, 503, 1873, 3449, 5231, 7219, 9413, 11813, 14419, 17231, 20249, 23473, 26903
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
This polynomial is a transformed version of the polynomial P(x) = 103*x^2 + 31*x - 3391 whose absolute value gives 43 distinct primes for -23 <= x <= 19, found by G. W. Fung in 1988. - Hugo Pfoertner, Dec 13 2019
|
|
|
REFERENCES
|
Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
|
|
|
LINKS
|
Robert Price, Table of n, a(n) for n = 1..3885
François Dress and Michel Olivier, Polynômes prenant des valeurs premières, Experimental Mathematics, Volume 8, Issue 4 (1999), 319-338.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials
|
|
|
EXAMPLE
|
33203 is in this sequence since 103*4^2 - 4707*4 + 50383 = 1648-18828+50383 = 33203 is prime.
|
|
|
MATHEMATICA
|
n = Range[0, 100]; Abs @ Select[103n^2 - 4707n + 50383 , PrimeQ[#] &]
|
|
|
PROG
|
(PARI) lista(nn) = for(n=0, nn, if(isprime(p=abs(103*n^2-4707*n+50383)), print1(p, ", "))); \\ Altug Alkan, Apr 28 2016, corrected by Hugo Pfoertner, Dec 13 2019
|
|
|
CROSSREFS
|
Cf. A050268, A050267, A005846, A007641, A007635, A048988, A050265, A050266.
Cf. A271980, A272030, A272074, A272075, A272118, A272159, A271143, A272284, A272323, A267069, A330363.
Sequence in context: A105001 A237949 A251466 * A166760 A231918 A029823
Adjacent sequences: A267249 A267250 A267251 * A267253 A267254 A267255
|
|
|
KEYWORD
|
nonn,less
|
|
|
AUTHOR
|
Robert Price, Apr 28 2016
|
|
|
EXTENSIONS
|
Title corrected by Hugo Pfoertner, Dec 13 2019
|
|
|
STATUS
|
approved
|
| |
|
|
