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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.
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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: A069208 A066113 A081836 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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njas
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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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