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Search: id:A165242
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| A165242 |
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The larger member of the n-th twin prime, modulo 8. |
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1
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| 5, 7, 5, 3, 7, 3, 5, 1, 7, 5, 3, 7, 5, 1, 7, 5, 1, 7, 3, 1, 5, 5, 1, 7, 3, 3, 1, 3, 3, 5, 3, 7, 5, 3, 3, 5, 1, 3, 7, 5, 1, 7, 7, 3, 7, 1, 5, 5, 3, 1, 1, 5, 5, 3, 3, 5, 1, 7, 5, 7, 7, 5, 3, 1, 1, 3, 7, 7, 5, 7, 5, 7, 7, 1, 3, 1, 1, 3, 7, 3, 3, 1, 1, 1, 5, 3, 5, 3, 1, 5, 7, 7, 5, 1, 5, 7, 7, 1, 1, 7, 5, 7, 3, 3, 5
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Related to the rank of some elliptic curves by the conjecture on page 2 of [Hatley]:
Let E_p be the elliptic curve defined by y^2 = x(x-p)(x-2) where p and p-2 are twin primes.
Then Rank(E_p) = 0 if p == 7 mod 8, 1 if p == 3,5 mod 8, 2 if p == 1 mod 8.
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REFERENCES
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Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.
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LINKS
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Jeffrey Hatley, On the Rank of the Elliptic Curve y^2=x(x-p)(x-2), arXiv:0909.1614 Sep 9, 2009.
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FORMULA
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a(n) = A010877(A006512(n)).
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MAPLE
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A006512 := proc(n) if n = 1 then 5; else for a from procname(n-1)+2 by 2 do if isprime(a) and isprime(a-2) then RETURN(a) ; fi; od: fi; end:
A165242 := proc(n) A006512(n) mod 8 ; end: seq(A165242(n), n=1..120) ; # R. J. Mathar, Sep 16 2009
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CROSSREFS
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Cf. A000040, A001359, A010877.
Sequence in context: A096458 A002338 A123489 this_sequence A104542 A161376 A107437
Adjacent sequences: A165239 A165240 A165241 this_sequence A165243 A165244 A165245
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 09 2009
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EXTENSIONS
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Redefined for the larger member of twin primes - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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