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A002335
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Numbers y such that p = x^2 - 2y^2.
(Formerly M0139 N0055)
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1
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1, 1, 2, 1, 3, 2, 1, 5, 2, 1, 4, 6, 3, 2, 7, 4, 3, 1, 7, 4, 9, 1, 8, 5, 10, 4, 7, 3, 2, 5, 8, 12, 2, 1, 9, 11, 8, 4, 7, 2, 1, 14, 6, 9, 5, 11, 13, 2, 14, 16, 4, 11, 8, 3, 2, 7, 10, 17, 12, 11, 1, 7, 13, 10, 6, 4, 3, 1, 16, 7, 20, 13, 5, 15, 4, 12, 2, 21, 14, 11, 7, 16, 13, 18, 5, 20, 9, 1, 8, 17, 14
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| 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
| 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
| with(numtheory): readlib(issqr):for i from 1 to 300 do p:=ithprime(i): pmod8:=modp(p, 8): if p=2 or pmod8=1 or pmod8=7 then for y from 1 do if issqr(p+2*y^2) then printf("%d, ", y): break fi od fi od: (Pab Ter)
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CROSSREFS
| Cf. A002334, A035251.
Sequence in context: A136451 A066121 A039911 * A173302 A179314 A204927
Adjacent sequences: A002332 A002333 A002334 * A002336 A002337 A002338
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 22 2005
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