a(n) is the least prime p such that q-p = n*(r-q) where p,q,r are consecutive primes.

Terms

a(0) =3a(1) =7a(2) =23a(3) =6397a(4) =139a(5) =509a(6) =84871a(7) =1933a(8) =1259a(9) =43331a(10) =1129a(11) =4523a(12) =933073a(13) =2971a(14) =6917a(15) =1568771a(16) =9973a(17) =32261a(18) =4131109a(19) =25261a(20) =78737a(21) =12809359a(22) =91033a(23) =28229a(24) =13626257a(25) =35677a(26) =117443a(27) =37305713a(28) =399793a(29) =102701