a(1) = 2, a(2) = 3, a(n+1) = least prime of the form k*(a(n-1)) - a(n) not included earlier.

Terms

a(0) =2a(1) =3a(2) =5a(3) =7a(4) =13a(5) =29a(6) =23a(7) =151a(8) =79a(9) =223a(10) =251a(11) =641a(12) =1367a(13) =3761a(14) =4441a(15) =78301a(16) =1637a(17) =311567a(18) =6011a(19) =8094731a(20) =32141a(21) =161862479a(22) =321007a(23) =2589478657a(24) =1047833a(25) =46609567993a(26) =52531163a(28) =803034293a(30) =17747231531