A162336 Primes p of the form p = r+(r+1)/2 (where r is a prime number).

5, 11, 17, 29, 47, 71, 89, 101, 107, 191, 197, 227, 251, 269, 317, 359, 461, 467, 521, 569, 647, 659, 701, 719, 821, 857, 881, 911, 929, 947, 971, 1091, 1109, 1181, 1217, 1259, 1289, 1361, 1367, 1451, 1487, 1559, 1637, 1847, 1889, 1979, 2099, 2141, 2207

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 01 2009

Keywords

• nonn

Comments

Or primes of the form Sum_{x=1..n-th prime} (1-(-1)^x*x). - Juri-Stepan Gerasimov, Jul 14 2009

Primes p such that (2*p-1)/3 is prime. - J. M. Bergot, Aug 19 2020

Examples

			3+2=5, 7+4=11, 11+6=17, 19+10=29, 31+16=47, 47+24=71,.. r:3,7,11,19,31,47,59,67,71,127,131,151,167,179,211,239,307,311, ..A158709.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A158709.

Programs

Maple

filter:= p -> isprime(p) and isprime((2*p-1)/3):
select(filter, [seq(i,i=5..10000,6)]); # Robert Israel, Aug 19 2020

Mathematica

lst={};Do[r=Prime[n];p=r+(r+1)/2;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst
Select[#+(#+1)/2&/@Prime[Range[300]],PrimeQ] (* Harvey P. Dale, Apr 30 2015 *)

Extensions

Edited by N. J. A. Sloane, Jul 18 2009