Smallest prime p(i) such that between 2p(i) and 2p(i+1) there exist n primes.

Terms

a(0) =59a(1) =2a(2) =5a(3) =31a(4) =89a(5) =509a(6) =113a(7) =1129a(8) =1951a(9) =7253a(10) =19609a(11) =16141a(12) =13339a(13) =28229a(14) =1327a(15) =281431a(16) =396733a(17) =1122287a(18) =461717a(19) =370261a(20) =2010733a(21) =492113a(22) =3279841a(23) =14246971a(24) =3117299a(25) =5826001a(26) =20831323a(27) =47326693a(28) =60487759a(29) =189695659