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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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D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
A. J. C. Cunningham, Quadratic Partitions. Hodgson, London, 1904, p. 1.
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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: A114255 A138579 A109624 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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njas
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