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

Author

Hugo Pfoertner, May 20 2018

Keywords

• nonn

Examples

			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.

Programs

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

Formula

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