a(n) is the smallest prime that is the sum of both 2n-1 and 2n+1 consecutive primes.

Terms

a(0) =23a(1) =83a(2) =311a(3) =401a(4) =1367a(5) =3617a(6) =863a(7) =5683a(8) =1523a(9) =153113a(10) =90011a(11) =10949a(12) =7901a(13) =155671a(14) =11131a(15) =117977a(16) =14699a(17) =252079a(18) =58369a(19) =132749a(20) =203293a(21) =641867a(22) =116257a(23) =607093a(24) =78791a(25) =46471a(26) =927049a(27) =340601a(28) =1485541a(29) =521897