A155962 Numbers n with property that 3*(2n)^2+1 and 1*(2n)^2+3 are primes.

1, 4, 11, 32, 56, 73, 80, 109, 122, 143, 158, 175, 182, 217, 256, 262, 280, 284, 290, 308, 343, 347, 403, 431, 434, 437, 535, 581, 598, 619, 655, 665, 928, 973, 980, 1018, 1036, 1046, 1096, 1120, 1159, 1207, 1222, 1235, 1267, 1382, 1393, 1439, 1460, 1463, 1501

Offset

1,2

Comments

2*A155962 is intersection of A049422 and A111051.

Links

Zak Seidov, Table of n,a (n) for n=1..1000

Example

n=1, {3*(2n)^2+1, 1*(2n)^2+3}={13,7};
n=4, {3*(2n)^2+1, 1*(2n)^2+3}={193,67};
n=11, {3*(2n)^2+1, 1*(2n)^2+3}={1453,487};
n=32, {3*(2n)^2+1,1*(2n)^2+3}={12289,4099}.
Resulting primes are congruent to 1 mod 3.

Mathematica

Select[Range[1600], AllTrue[{3(2#)^2+1, (2#)^2+3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 30 2016 *)

Crossrefs

Cf. A049422, A111051.

Sequence in context: A076730 A084757 A353425 * A027153 A319918 A034754

Adjacent sequences: A155959 A155960 A155961 * A155963 A155964 A155965

Keyword

nonn

Author

Zak Seidov, Jan 31 2009

Extensions

All the terms in the b-file had to be divided by 2. Corrected by N. J. A. Sloane, Aug 31 2009.

Status

approved