A158709 Primes p such that p + ceiling(p/2) is prime.

2, 3, 7, 11, 19, 31, 47, 59, 67, 71, 127, 131, 151, 167, 179, 211, 239, 307, 311, 347, 379, 431, 439, 467, 479, 547, 571, 587, 607, 619, 631, 647, 727, 739, 787, 811, 839, 859, 907, 911, 967, 991, 1039, 1091, 1231, 1259, 1319, 1399, 1427, 1471, 1511, 1531, 1559

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 24 2009

Keywords

• nonn
• easy

Comments

Or, 2 along with primes p such that Sum_{x=1..p} (1 - (-1)^x*x) is prime. - Juri-Stepan Gerasimov, Jul 14 2009

Apart from the first term, primes of the form 4*k-1 such that 6*k-1 is also prime. - Charles R Greathouse IV, Nov 09 2011

If both p and q are in A158709 and p + q == 2 (mod 4), then A006370(A006370(p + q)) = A006370((p + q)/2) = 3*(p + q)/2 + 1 is the sum of the two primes p+ceiling(p/2) and q+ceiling(q/2). - Roderick MacPhee, Feb 23 2018

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A158708.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[Ceiling[p/2]+p],AppendTo[lst,p]],{n,6!}];lst
Select[Prime@ Range@ 250, PrimeQ@ Ceiling[3#/2] &] (* Vincenzo Librandi, Apr 15 2013 and slightly modified by Robert G. Wilson v, Feb 26 2018 *)

PARI

forprime(p=2,1e4,if(isprime(p+ceil(p/2)),print1(p", "))) \\ Charles R Greathouse IV, Nov 09 2011

PARI

print1(2);forprime(p=3,1e4,if(p%4==3&&isprime(p\4*6+5),print1(", "p))) \\ Charles R Greathouse IV, Nov 09 2011

Extensions

Corrected by Charles R Greathouse IV, Mar 18 2010