The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A304905 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A304905

Greatest difference d such that both n^2 - d and n^2 + d are primes.
(history; published version)

#6 by Susanna Cuyler at Sun May 20 18:03:12 EDT 2018

STATUS

proposed

approved

#5 by Felix Fröhlich at Sun May 20 17:31:28 EDT 2018

STATUS

editing

proposed

#4 by Felix Fröhlich at Sun May 20 17:29:56 EDT 2018

PROG

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

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

STATUS

proposed

editing

#3 by Hugo Pfoertner at Sun May 20 13:13:17 EDT 2018

STATUS

editing

proposed

#2 by Hugo Pfoertner at Sun May 20 13:01:59 EDT 2018

NAME

allocated for Hugo PfoertnerGreatest difference d such that both n^2 - d and n^2 + d are primes.

DATA

1, 4, 13, 22, 31, 30, 45, 76, 97, 118, 139, 162, 193, 218, 253, 282, 319, 358, 397, 436, 453, 522, 553, 612, 645, 724, 765, 828, 889, 918, 1005, 1072, 1153, 1222, 1283, 1362, 1413, 1516, 1587, 1678, 1753, 1842, 1917

OFFSET

2,2

FORMULA

a(n) = (A304904(n) - A304903(n))/2 = n^2 - A304903(n) = A304904(n) - n^2.

EXAMPLE

a(2) = 1 because 2^2 - 1 = 3 and 2^2 + 1 = 5 are primes.

a(7) = 30 because 7^2 - 30 = 19 and 7^2 + 30 = 79 is the pair with maximum difference. All greater differences lead to at least one composite, i.e., 49 + 32 = 81, 49 - 34 = 15, 49 + 36 = 85, 49 + 38 = 87, 49 - 40 = 9, 49 + 42 = 91 = 7*13, 49 + 44 = 93 = 3*31, 49 + 46 = 95, and 49 - 48 = 1 is not a prime.

CROSSREFS

Cf. A172989, A304903, A304904.

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