a(n) = 2*a(n-1) - a(n-2) + 2*(prime(n+1)-prime(n)); a(1) = 2, a(2) = 3.

Terms

a(0) =2a(1) =3a(2) =8a(3) =21a(4) =38a(5) =63a(6) =92a(7) =129a(8) =178a(9) =231a(10) =296a(11) =369a(12) =446a(13) =531a(14) =628a(15) =737a(16) =850a(17) =975a(18) =1108a(19) =1245a(20) =1394a(21) =1551a(22) =1720a(23) =1905a(24) =2098a(25) =2295a(26) =2500a(27) =2709a(28) =2926a(29) =3171