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

0,1

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

Links

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

Formula

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

Example

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.

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}]

Crossrefs

Cf. A087711.

Sequence in context: A057264 A045514 A102957 * A176450 A263345 A181655

Adjacent sequences: A216895 A216896 A216897 * A216899 A216900 A216901

Keyword

nonn

Author

Zak Seidov, Sep 19 2012

Status

approved