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A165242
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The larger member of the n-th twin prime pair, 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
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OFFSET
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1,1
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COMMENTS
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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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FORMULA
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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:
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MATHEMATICA
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Mod[#, 8]&/@(Select[Partition[Prime[Range[800]], 2, 1], #[[2]]-#[[1]]==2&][[All, 2]]) (* Harvey P. Dale, Sep 26 2016 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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Redefined for the larger member of twin primes by R. J. Mathar, Sep 16 2009
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STATUS
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approved
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