A201478 Primes of the form 3n^2 + 5.

5, 17, 53, 113, 197, 593, 773, 977, 1733, 2357, 4337, 5297, 5813, 6353, 6917, 8117, 8753, 9413, 13877, 16433, 17333, 18257, 20177, 22193, 26513, 27653, 28817, 33713, 38993, 41777, 44657, 46133, 49157, 60497, 62213, 65717, 69317, 71153

Offset

1,1

Comments

Starting at a(3) all primes in this sequence are of the form (2*k+1)*(2*k+3)+(2*k+3)*(2*k+5)+(2*k+5)*(2*k+7) = 12*k^2 + 48*k + 53 for some k >= 0. For example a(5) = 5*7 + 7*9 + 9*11 = 197. - J. M. Bergot, Nov 03 2014

Links

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

Mathematica

Select[Table[3n^2 + 5, {n, 0, 700}], PrimeQ]

Prog

(Magma) [a: n in [0..400] | IsPrime(a) where a is 3*n^2+5];
(PARI) select(isprime, vector(100, n, 3*n^2+5)) \\ Charles R Greathouse IV, Nov 05 2014

Crossrefs

Sequence in context: A090575 A191139 A107167 * A176470 A240693 A278464

Adjacent sequences: A201475 A201476 A201477 * A201479 A201480 A201481

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 02 2011

Status

approved