A283867 Numbers n such that 30*n^2 - 1 and 30*n^2 + 1 are (twin) primes.

1, 3, 10, 14, 18, 38, 62, 73, 116, 118, 143, 183, 221, 232, 242, 330, 333, 413, 430, 455, 470, 496, 507, 533, 538, 556, 606, 622, 645, 675, 687, 701, 720, 777, 792, 819, 846, 879, 881, 895, 913, 1000, 1019, 1030, 1092, 1155, 1214, 1238, 1253, 1261, 1313, 1337, 1350, 1407, 1418, 1429, 1431

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 17 2017

Keywords

• nonn

Examples

			3 is in this sequence because 30*3^2 - 1 = 269 and 30*3^2 + 1 = 271 are twin primes.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A001097, A077800, A158558, A158560.

Programs

Magma

[n: n in [1..1500] | IsPrime(30*n^2-1) and IsPrime(30*n^2+1)];

Mathematica

Select[Range@ 1431, PrimeQ[30*#^2 + 1] && PrimeQ[30*#^2 - 1] &] (* Indranil Ghosh, Mar 17 2017 *)

PARI

is(n)=isprime(30*n^2-1) && isprime(30*n^2+1) \\ Charles R Greathouse IV, Mar 17 2017

Python

from sympy import isprime
[i for i in range(1, 1501) if isprime(30*i**2 - 1) and isprime(30*i**2 + 1)] # Indranil Ghosh, Mar 17 2017

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Mar 17 2017