a(n) = the first prime in the earliest sequence of 2n+1 consecutive primes whose average is prime.

Terms

a(0) =3a(1) =71a(2) =7a(3) =463a(4) =31a(5) =43a(6) =5a(7) =7a(8) =499a(9) =821a(10) =109a(11) =97a(12) =271a(13) =263a(14) =179a(15) =97a(16) =181a(17) =47a(18) =233a(19) =1931a(20) =359a(21) =227a(22) =1787a(23) =443a(24) =29a(25) =131a(26) =1061a(27) =229a(28) =599a(29) =1931