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A098828
Primes of the form 3x^2 - y^2, where x and y are two consecutive numbers.
7
3, 11, 23, 59, 83, 179, 263, 311, 419, 479, 683, 839, 1103, 1511, 2111, 2243, 2663, 2963, 3119, 4139, 4703, 5099, 5303, 5939, 7079, 10223, 11399, 12011, 12323, 12959, 17483, 19403, 21011, 21839, 22259, 24419, 25763, 27143, 27611, 28559, 30011
OFFSET
1,1
COMMENTS
Equivalently primes of the form 2n^2 - 2n - 1. a(n)==3 (mod 4).
Equivalently primes p such that 2p+3 is square.
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
LINKS
FORMULA
a(n) = (A109367(n) - 3)/2.
MATHEMATICA
Select[Table[Prime[n], {n, 3500}], IntegerQ[(2# + 3)^(1/2)] &] (* Ray Chandler, Oct 26 2004 *)
PROG
(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^(p-1)+3) ];
CROSSREFS
Sequence in context: A289888 A145477 A243887 * A165635 A376753 A337476
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto, Oct 09 2004
EXTENSIONS
Corrected by Ray Chandler, Oct 26 2004
Edited by N. J. A. Sloane, Jan 25 2009
STATUS
approved