A306627 - OEIS

%I #18 Mar 11 2019 09:28:48

%S 43,53,79,97,199,257,347,1103,1187,1303,1367,1753,2029,2351,2593,2647,

%T 3181,3253,4663,4787,4903,4919,5573,6091,7079,7331,7369,7457,8101,

%U 8527,8543,10159,11549,12647,13151,14699,15031,15559,15679,15881,15889,16661,17099,17881,18251,18959,19219,20399,20431

%N Primes of the form (p + prime(p))/2 with prime p.

%C Indices k of p's are 8, 9, 11, 12, 19, 23, 28, 62, 64, 68, 71, 85, 95, 104, 114, 115, 131, 134, 175, 178, 181, 182, 200, 216, 240, 246, 247, 250, 266, 276, 277, 316, 346, 372, 382.

%C And some of k's themselves are prime: 11, 19, 23, 71, 131, 181, 277, 421, 541, 601, 673, 751, 881, 937. See link to Fernandez.

%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html"> An order of primeness</a>

%e 43 = (p + prime(p))/2 for p = 19 (prime),

%e 53 = (p + prime(p))/2 for p = 23 (prime).

%o (PARI) lista(nn) = forprime(p=3,nn,k=(prime(p)+p)/2;if(isprime(k),print1(k, ", "))) \\ _Jinyuan Wang_, Mar 01 2019

%Y Cf. A014688 (n-th prime + n).

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 01 2019