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A165242 The larger member of the n-th twin prime pair, modulo 8. 1
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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).

REFERENCES

Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

LINKS

Table of n, a(n) for n=1..105.

Jeffrey Hatley, On the Rank of the Elliptic Curve y^2=x(x-p)(x-2), arXiv:0909.1614 [math.NT], 2009.

FORMULA

a(n) = A010877(A006512(n)).

MAPLE

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

MATHEMATICA

Mod[#, 8]&/@(Select[Partition[Prime[Range[800]], 2, 1], #[[2]]-#[[1]]==2&][[All, 2]]) (* Harvey P. Dale, Sep 26 2016 *)

CROSSREFS

Cf. A000040, A001359, A010877.

Sequence in context: A178668 A198744 A201944 * A104542 A161376 A107437

Adjacent sequences:  A165239 A165240 A165241 * A165243 A165244 A165245

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 09 2009

EXTENSIONS

Redefined for the larger member of twin primes by R. J. Mathar, Sep 16 2009

STATUS

approved

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Last modified October 18 13:31 EDT 2019. Contains 328161 sequences. (Running on oeis4.)