Average of a twin prime pair which is the sum of the first k primes, for some k.

Terms

a(0) =6870a(1) =25800a(2) =38238a(3) =125508a(4) =128112a(5) =220512a(6) =372612a(7) =3245688a(8) =4286748a(9) =15433968a(10) =19659138a(11) =23283852a(12) =23494650a(13) =23579262a(14) =26233368a(15) =32131272a(16) =32380728a(17) =34775988a(18) =41299848a(19) =58705260a(20) =61470132a(21) =63588432a(22) =63873960a(23) =91649652a(24) =92774808a(25) =106956252a(26) =124336212a(27) =159723300