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Search: id:A002343
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| A002343 |
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Least positive integer y 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 M0109 N0042)
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+0
2
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| 1, 1, 1, 1, 2, 1, 2, 3, 1, 3, 1, 4, 1, 1, 2, 4, 5, 5, 1, 2, 3, 6, 3, 1, 5, 2, 4, 1, 7, 5, 3, 5, 7, 1, 5, 7, 3, 1, 4, 5, 6, 8, 1, 2, 7, 9, 4, 5, 3, 5, 2, 1, 9, 5, 6, 7, 10, 11, 3, 1, 4, 11, 6, 7, 8, 9, 7, 1, 4, 9, 5, 3, 8, 13, 3, 1, 4, 11, 1, 8, 2, 9, 10, 11, 13, 14, 7, 4, 5, 11, 7, 2, 10, 11, 15, 5, 9
(list; graph; listen)
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OFFSET
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1,5
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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)=1, 11=(7^2-5*1^2)/4 so a(2)=1.
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PROGRAM
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(PARI) a(n)=local(y, p); if(n<1, 0, p=0; y=1; until(p>=n, y++; if(issquare(5+O(prime(y))), p++)); p=prime(y); y=0; until(issquare(4*p+5*y^2), y++); y)
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CROSSREFS
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Cf. A002342.
Cf. A002342, A038872.
Sequence in context: A126247 A101161 A097825 this_sequence A082076 A048793 A075106
Adjacent sequences: A002340 A002341 A002342 this_sequence A002344 A002345 A002346
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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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