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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 (list; graph; refs; listen; history; text; internal format)
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

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)] &] (*Chandler*)

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

Cf. A109358, A109367.

Cf. A153238

Sequence in context: A289888 A145477 A243887 * A165635 A032026 A282198

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

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Last modified July 25 15:34 EDT 2017. Contains 289795 sequences.