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A152460 Primes p such that there exist positive integer k and prime q with p > q and 3^k = p + 2q or 3^k = q + 2p. 1

%I

%S 3,5,11,13,17,23,29,31,37,43,47,59,67,71,97,101,103,107,109,113,137,

%T 149,157,181,197,229,233,239,251,263,269,271,281,283,307,311,313,331,

%U 347,349,353,359,367,383,431,467,503,523,563,571,587,607,643,647,683,691

%N Primes p such that there exist positive integer k and prime q with p > q and 3^k = p + 2q or 3^k = q + 2p.

%C a(n) is the greater of primes (p,q) in representations of a power of 3 in Lemoine-Levy's form p+2q (see A046927)

%C If 3^n=p+2q, then 3^(n-1)<=max(p,q)<3^n. Therefore the sets of greater primes for different powers of 3 do not intersect.

%F If A(x) is the counting function of a(n)<=x, then A(x)=O(xloglogx/(logx)^2).

%e 27=5+2*11=13+2*7=17+2*5=23+2*2, so that 11,13,17 and 23 are in the sequence.

%o (PARI) aa(n)={my(v=[]); forprime(p=2,n\2,q=n-p*2; if(isprime(q),v=concat(v,(max(p,q))))); vecsort(v,,8)};

%o for(n=2, 7, v=aa(3^n); for(i=1,#v,print1(v[i], ", ")))

%Y Cf. A103151, A086081, A152451

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Dec 05 2008, Dec 12 2008

%E Program and editing by _Charles R Greathouse IV_, Nov 02 2009

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Last modified November 19 06:26 EST 2019. Contains 329310 sequences. (Running on oeis4.)