A201716 Primes of the form 3*m^2 - 4.

23, 71, 239, 359, 503, 863, 1319, 1583, 1871, 2879, 3671, 5039, 8423, 9743, 11159, 11903, 12671, 13463, 16871, 17783, 18719, 20663, 25943, 29399, 33071, 38303, 39671, 48383, 49919, 51479, 61343, 68399, 70223, 73943, 81671, 83663, 87719

Offset

1,1

Comments

Primes p such that 3*(p+4) or (p+4)/3 is a square. - Vincenzo Librandi, Dec 05 2015, Feb 16 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Example

23 is in the sequence because 3 * 3^2 - 4 = 27 - 4 = 23.
71 = 3 * 5^2 - 4.
143 is not in the sequence, because 3 * 7^2 - 4 = 143 but 11 * 13 = 143.

Maple

select(isprime, [seq(3*(2*k+1)^2-4, k = 1..1000)]); # Robert Israel, Nov 09 2014

Mathematica

Select[Table[3n^2 - 4, {n, 1000}], PrimeQ]

Prog

(Magma) [a: n in [1..300] | IsPrime(a) where a is 3*n^2-4];
(PARI) lista(nn) = for (k=0, nn, if (isprime(p=3*k^2-4), print1(p, ", "))); \\ Michel Marcus, Nov 19 2014, Feb 16 2016

Crossrefs

Cf. A089682, A201715, A201717, A201718, A201781.

Sequence in context: A321356 A139878 A035072 * A269521 A044161 A044542

Adjacent sequences: A201713 A201714 A201715 * A201717 A201718 A201719

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 04 2011

Status

approved