A228830 Primes p(n) such that 2*p(n) + p(2n) is prime.
2, 3, 5, 23, 37, 43, 59, 89, 103, 127, 149, 151, 163, 197, 199, 277, 347, 379, 409, 443, 449, 487, 617, 619, 631, 641, 643, 823, 829, 853, 859, 887, 929, 953, 997, 1069, 1151, 1181, 1303, 1321, 1381, 1493, 1499, 1543, 1583, 1613, 1637, 1747, 1867, 1889, 2027, 2053
Offset: 1
Keywords
Examples
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. 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. 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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A228727.
Programs
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Mathematica
Prime[Select[Range[300], PrimeQ[2Prime[#] + Prime[2#]] &]] (* Alonso del Arte, Sep 08 2013 *) Select[Prime[Range[350]],PrimeQ[2#+Prime[2PrimePi[#]]]&] (* Harvey P. Dale, Mar 11 2019 *)
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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
Extensions
Terms corrected by Charles R Greathouse IV, Sep 05 2013