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A165242 The larger member of the n-th twin prime pair, modulo 8. 1

%I

%S 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,

%T 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,

%U 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

%N The larger member of the n-th twin prime pair, modulo 8.

%C Related to the rank of some elliptic curves by the conjecture on page 2 of [Hatley]:

%C Let E_p be the elliptic curve defined by y^2 = x(x-p)(x-2) where p and p-2 are twin primes.

%C Then Rank(E_p) = 0 if p == 7 (mod 8), 1 if p == 3,5 (mod 8), 2 if p == 1 (mod 8).

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

%H Jeffrey Hatley, <a href="http://arxiv.org/abs/0909.1614">On the Rank of the Elliptic Curve y^2=x(x-p)(x-2)</a>, arXiv:0909.1614 [math.NT], 2009.

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

%p 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:

%p A165242 := proc(n) A006512(n) mod 8 ; end: seq(A165242(n),n=1..120) ; # _R. J. Mathar_, Sep 16 2009

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

%Y Cf. A000040, A001359, A010877.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Sep 09 2009

%E Redefined for the larger member of twin primes by _R. J. Mathar_, Sep 16 2009

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)