|
| |
|
|
A080020
|
|
Primes of the form 9n^2 + 3n + 367 for any integer n.
|
|
2
| |
|
|
367, 373, 379, 397, 409, 439, 457, 499, 523, 577, 607, 673, 709, 787, 829, 919, 967, 1069, 1123, 1237, 1297, 1423, 1489, 1627, 1699, 2089, 2347, 2437, 2719, 2917, 3019, 3229, 3559, 3673, 3907, 4027, 4273, 4657, 4789, 5059, 5197, 5479, 5623, 6067, 6373
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Original definition: Primes of the form q(n) = 370 + 18*binomial(ceiling(n/2),2) + 3*(-1)^n*(2*ceiling(n/2)-1).
The smallest positive n for which q(n) is not prime is n=26.
Every q(n) is a divisor of some value of e(x) = x^2+x+41, the Euler prime-generating polynomial. Specifically, e(3*n^2-2*n+122) = q(2*n) * e(n-1) and e(3*n^2+2*n+122) = q(2*n+1) * e(n).
|
|
|
LINKS
| Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
|
|
|
CROSSREFS
| Cf. A005846.
Sequence in context: A073305 A033174 A079493 * A192448 A118566 A142236
Adjacent sequences: A080017 A080018 A080019 * A080021 A080022 A080023
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Tewodros Amdeberhan (tewodros(AT)math.temple.edu), Jan 20 2003
|
|
|
EXTENSIONS
| Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Jan 20 2003
New definition from Charles R Greathouse IV, Feb 15 2011
|
| |
|
|
