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A098828
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Primes of the form 3x^2 - y^2, where x and y are two consecutive numbers.
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5
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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; internal format)
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OFFSET
| 1,1
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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 such that 2^(p-1)+3 is not prime. - Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jan 03 2009; M. F. Hasler, Jan 07 2009; R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 14 2009.
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FORMULA
| a(n) = (A109367(n) - 3)/2.
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MATHEMATICA
| Select[Table[Prime[n], {n, 3500}], IntegerQ[(2# + 3)^(1/2)] &] (*Chandler*)
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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) ];
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CROSSREFS
| Cf. A109358, A109367.
Cf. A153238
Sequence in context: A173078 A128928 A145477 * A165635 A032026 A158034
Adjacent sequences: A098825 A098826 A098827 * A098829 A098830 A098831
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KEYWORD
| nonn
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AUTHOR
| Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Oct 09 2004
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EXTENSIONS
| Corrected by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 26 2004
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 25 2009
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