A216898 a(n) = smallest number k such that both k - n^2 and k + n^2 are primes.

2, 4, 7, 14, 21, 28, 43, 52, 67, 86, 111, 150, 149, 180, 201, 232, 267, 312, 329, 366, 411, 446, 487, 532, 587, 654, 705, 742, 787, 852, 911, 972, 1029, 1118, 1185, 1242, 1313, 1372, 1473, 1528, 1603, 1692, 1769, 1852, 1941, 2032, 2127, 2212, 2317, 2412, 2503

Offset: 0

Author

Zak Seidov, Sep 19 2012

Keywords

• nonn

Comments

Note that a(11) = 150 and a(12) = 149. Up to n = 10^6, this is the only case where a(n) > a(n+1). What about general case of a(n) < a(n+1)?

First differences are almost linear with n hence the only case with a(n) > a(n+1) is n = 11. - Zak Seidov, May 19 2014

Examples

			a(11) = 150 because both 150 - 11^2 = 29 and 150 + 11^2 = 271 are primes.
a(12) = 149 because both 149 - 12^2 = 5 and 149 + 12^2 = 293 are primes.
		

Links

• Zak Seidov, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A087711.

Programs

Mathematica

Table[If[n < 1, 2, m = n^2 + 1; While[!PrimeQ[m - n^2] || !PrimeQ[m + n^2], m = m + 2]; m], {n, 0, 100}]

Formula

a(n) = A087711(n^2). - T. D. Noe, Sep 19 2012