

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
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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)^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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000


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^(p1)+3) ];


CROSSREFS

Cf. A109358, A109367.
Cf. A153238
Sequence in context: A289888 A145477 A243887 * A165635 A337476 A301876
Adjacent sequences: A098825 A098826 A098827 * A098829 A098830 A098831


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



