%I
%S 3,11,23,59,83,179,263,311,419,479,683,839,1103,1511,2111,2243,2663,
%T 2963,3119,4139,4703,5099,5303,5939,7079,10223,11399,12011,12323,
%U 12959,17483,19403,21011,21839,22259,24419,25763,27143,27611,28559,30011
%N Primes of the form 3x^2  y^2, where x and y are two consecutive numbers.
%C Equivalently primes of the form 2n^2  2n  1. a(n)==3 (mod 4).
%C Equivalently primes p such that 2p+3 is square.
%C Also 3 followed by primes p of the form 2*n^2+6*n+3 = 2*(n+2)^22*(n+2)1 (see the first comment) such that 2^(p1)+3 is not prime.  _Vincenzo Librandi_, Jan 03 2009; M. F. Hasler, Jan 07 2009; _R. J. Mathar_, Jan 14 2009; _Bruno Berselli_, Sep 23 2013
%H Vincenzo Librandi, <a href="/A098828/b098828.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = (A109367(n)  3)/2.
%t Select[Table[Prime[n], {n, 3500}], IntegerQ[(2# + 3)^(1/2)] &] (* _Ray Chandler_, Oct 26 2004 *)
%o (MAGMA) [3] cat [ p: p in PrimesUpTo(30100)  exists(t){ n: n in [1..Isqrt(p div 2)]  2*n^2+6*n+3 eq p } and not IsPrime(2^(p1)+3) ];
%Y Cf. A109358, A109367.
%Y Cf. A153238
%K nonn
%O 1,1
%A _Giovanni Teofilatto_, Oct 09 2004
%E Corrected by _Ray Chandler_, Oct 26 2004
%E Edited by _N. J. A. Sloane_, Jan 25 2009
