Numbers p such that p = (prime(n)+ prime(n+2))/2 is prime for prime indices n=2, 3, 5...

Terms

a(0) =5a(1) =373a(2) =593a(3) =1223a(4) =1511a(5) =1747a(6) =2903a(7) =4409a(8) =5113a(9) =5387a(10) =5563a(11) =5807a(12) =6317a(13) =6367a(14) =9871a(15) =11933a(16) =12653a(17) =13043a(18) =13177a(19) =16097a(20) =18223a(21) =18731a(22) =20347a(23) =20731a(24) =22073a(25) =23893a(26) =24077a(27) =24677a(28) =28069a(29) =30097