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 A098828 Primes of the form 3x^2 - y^2, where x and y are two consecutive numbers. 7

%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)^2-2*(n+2)-1 (see the first comment) such that 2^(p-1)+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)  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^(p-1)+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

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Last modified May 18 23:08 EDT 2021. Contains 344008 sequences. (Running on oeis4.)