A304905 Greatest difference d such that both n^2 - d and n^2 + d are primes.

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

Links

Table of n, a(n) for n=2..44.

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.

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

Crossrefs

Cf. A172989, A304903, A304904.

Sequence in context: A063121 A199798 A153193 * A043469 A067396 A017209

Adjacent sequences: A304902 A304903 A304904 * A304906 A304907 A304908

Keyword

nonn

Author

Hugo Pfoertner, May 20 2018

Status

approved