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Primes p(n) such that 2*p(n) + p(2n) is prime.
1

%I #15 Mar 11 2019 16:03:22

%S 2,3,5,23,37,43,59,89,103,127,149,151,163,197,199,277,347,379,409,443,

%T 449,487,617,619,631,641,643,823,829,853,859,887,929,953,997,1069,

%U 1151,1181,1303,1321,1381,1493,1499,1543,1583,1613,1637,1747,1867,1889,2027,2053

%N Primes p(n) such that 2*p(n) + p(2n) is prime.

%H Charles R Greathouse IV, <a href="/A228830/b228830.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 is in the sequence, being the second prime, as we verify that 2 * prime(2) + prime(2 * 2) = 2 * 3 + 7 = 13, which is also prime.

%e 5 is in the sequence, being the third prime, as we see that 2 * prime(3) + prime(2 * 3) = 2 * 5 + 13 = 23, which is also prime.

%e 7 is not in the sequence, since it gives 2 * prime(4) + prime(2 * 4) = 2 * 7 + 19 = 33 = 3 * 11, which is not prime.

%t Prime[Select[Range[300], PrimeQ[2Prime[#] + Prime[2#]] &]] (* _Alonso del Arte_, Sep 08 2013 *)

%t Select[Prime[Range[350]],PrimeQ[2#+Prime[2PrimePi[#]]]&] (* _Harvey P. Dale_, Mar 11 2019 *)

%o (PARI) v=List(); n=q=0;forprime(p=2,1e4,if(n++%2,next); q=nextprime(q+1);if(isprime(2*q+p), listput(v,q))); Vec(v) \\ _Charles R Greathouse IV_, Sep 05 2013

%Y Cf. A228727.

%K nonn

%O 1,1

%A _Irina Gerasimova_, Sep 04 2013

%E Terms corrected by _Charles R Greathouse IV_, Sep 05 2013