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Primes of the form 3n^2 + 2.
1

%I #17 Sep 08 2022 08:46:12

%S 2,5,29,149,509,677,1877,3677,8429,9749,11909,13469,17789,22709,27077,

%T 28229,45389,46877,53069,70229,72077,81677,100469,102677,114077,

%U 128549,141269,154589,180077,192029,195077,207509,223589,230189,261077,312989,340709,352949,395309,399677,426389

%N Primes of the form 3n^2 + 2.

%C Two together with A027864(n).

%C Generated by n = 0, 1, 3, 7, 13, 15, 25, 35, 53, 57, ...

%e 2 is in this sequence because 3*0^2 + 2 = 2 and 2 is prime.

%t Select[Table[3 n^2 + 2, {n, 0, 400}], PrimeQ] (* _Vincenzo Librandi_, Apr 17 2015 *)

%o (Magma) [a: n in [0..400] | IsPrime(a) where a is (3*n^2+2)];

%o (PARI) select(isprime, vector(100, n, 3*n^2-6*n+5)) \\ _Charles R Greathouse IV_, Apr 17 2015

%Y Cf. A103564, A027864. Primes of the form k*n^2 + k - 1: A090698, this sequence, A121825, A201483, A201600, A201607, A201704.

%K nonn,easy

%O 1,1

%A _Juri-Stepan Gerasimov_, Apr 16 2015