The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304904 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A304904

Greatest prime p such that 2*n^2 - p is prime.
(history; published version)

#9 by Susanna Cuyler at Sun May 20 18:03:05 EDT 2018

STATUS

proposed

approved

#8 by Felix Fröhlich at Sun May 20 17:31:39 EDT 2018

STATUS

editing

proposed

#7 by Felix Fröhlich at Sun May 20 17:27:07 EDT 2018

PROG

(PARI) a304903(n) = forprime(p=3, , if(ispseudoprime(2*n^2-p), return(p)))

a(n) = 2*n^2-a304903(n) \\ Felix Fröhlich, May 20 2018

STATUS

proposed

editing

#6 by Hugo Pfoertner at Sun May 20 13:12:21 EDT 2018

STATUS

editing

proposed

#5 by Hugo Pfoertner at Sun May 20 13:11:48 EDT 2018

CROSSREFS

Cf. A304874, A204875, A304875, A304903, A304905.

#4 by Hugo Pfoertner at Sun May 20 12:32:40 EDT 2018

FORMULA

a(n) = n^2 + A304905(n) = A304903(n) + 2*A304905(n).

EXAMPLE

a(6) = 67 because 2*6^2 - 67 = 5 is prime whereas 72 - 71 = 1 is not a prime.

#3 by Hugo Pfoertner at Sun May 20 12:24:06 EDT 2018

COMMENTS

Each square > 1 can be written as the average of 2 primes p1 < p2. a(n) gives the greatest prime p2 such that n^2 = (p1 + p2) / 2. The corresponding p1 is provided in A304903.

#2 by Hugo Pfoertner at Sun May 20 12:20:56 EDT 2018

NAME

allocated for Hugo PfoertnerGreatest prime p such that 2*n^2 - p is prime.

DATA

5, 13, 29, 47, 67, 79, 109, 157, 197, 239, 283, 331, 389, 443, 509, 571, 643, 719, 797, 877, 937, 1051, 1129, 1237, 1321, 1453, 1549, 1669, 1789, 1879, 2029, 2161, 2309, 2447, 2579, 2731, 2857, 3037, 3187, 3359, 3517

OFFSET

2,1

CROSSREFS

Cf. A304874, A204875, A304903, A304905.

KEYWORD

allocated

nonn

AUTHOR

Hugo Pfoertner, May 20 2018

STATUS

approved

editing

#1 by Hugo Pfoertner at Sun May 20 11:54:21 EDT 2018

NAME

allocated for Hugo Pfoertner

KEYWORD

allocated

STATUS

approved