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.

3, 5, 11, 13, 17, 23, 29, 31, 37, 43, 47, 59, 67, 71, 97, 101, 103, 107, 109, 113, 137, 149, 157, 181, 197, 229, 233, 239, 251, 263, 269, 271, 281, 283, 307, 311, 313, 331, 347, 349, 353, 359, 367, 383, 431, 467, 503, 523, 563, 571, 587, 607, 643, 647, 683, 691

Offset: 1

Author

Vladimir Shevelev, Dec 05 2008, Dec 12 2008

Keywords

• nonn

Comments

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)

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.

Examples

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

Crossrefs

Cf. A103151, A086081, A152451

Programs

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

Formula

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

Extensions

Program and editing by Charles R Greathouse IV, Nov 02 2009