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Search: id:A002342
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| A002342 |
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Least positive integer x such that p=(x^2-5y^2)/4 where p is the n-th odd prime such that 5 is a square mod p.
(Formerly M3758 N1534)
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+0
2
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| 5, 7, 9, 11, 12, 13, 16, 17, 17, 19, 19, 22, 21, 23, 24, 26, 27, 29, 27, 28, 29, 32, 31, 31, 33, 32, 34, 33, 37, 37, 37, 39, 41, 39, 41, 43, 41, 41, 42, 43, 44, 46, 43, 44, 47, 49, 46, 47, 47, 49, 48, 49, 53, 51, 52, 53, 56, 57, 53, 53, 54, 59, 56, 57, 58, 59, 59, 57, 58, 61
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The n-th odd prime for which 5 is a square mod p is A038872(n).
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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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EXAMPLE
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5=(5^2-5*1^2)/4 so a(1)=5, 11=(7^2-5*1^2)/4 so a(2)=7.
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PROGRAM
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(PARI) a(n)=local(y, p); if(n<1, 0, p=0; y=2; until(p>=n, y++; if(issquare(5+O(prime(y))), p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2), y++); sqrtint(4*p+5*y^2))
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CROSSREFS
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Cf. A002343, A038872.
Sequence in context: A138579 A158251 A165513 this_sequence A080353 A128163 A106505
Adjacent sequences: A002339 A002340 A002341 this_sequence A002343 A002344 A002345
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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