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Search: id:A002334
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| A002334 |
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x such that p = x^2 - 2y^2.
(Formerly M0607 N0219)
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+0
2
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| 2, 3, 5, 5, 7, 7, 7, 11, 9, 9, 11, 13, 11, 11, 15, 13, 13, 13, 17, 15, 19, 15, 19, 17, 21, 17, 19, 17, 17, 19, 21, 25, 19, 19, 23, 25, 23, 21, 23, 21, 21, 29, 23, 25, 23, 27, 29, 23, 31, 33, 25, 29, 27, 25, 25, 27, 29, 35, 31, 31, 27, 29, 33, 31, 29, 29, 29, 29, 37, 31, 41, 35
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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A prime p is representable in the form x^2-2y^2 iff p is 2 or p == 1 or 7 mod 8. - Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005
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REFERENCES
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A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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MAPLE
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with(numtheory): readlib(issqr): for i from 1 to 250 do p:=ithprime(i): pmod8:=modp(p, 8): if p=2 or pmod8=1 or pmod8=7 then for y from 1 do x2:=p+2*y^2: if issqr(x2) then printf("%d, ", sqrt(x2)): break fi od fi od: (Pab Ter)
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CROSSREFS
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Cf. A002335.
Cf. A035251.
Sequence in context: A163831 A081836 A154290 this_sequence A115732 A048947 A114519
Adjacent sequences: A002331 A002332 A002333 this_sequence A002335 A002336 A002337
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004
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