a(1) = 5; a(n) for n > 1 is the smallest prime > a(n-1) that differs from a(n-1) by a square.

Terms

a(0) =5a(1) =41a(2) =617a(3) =653a(4) =797a(5) =941a(6) =977a(7) =1013a(8) =1049a(9) =1193a(10) =1229a(11) =1373a(12) =1409a(13) =1553a(14) =1697a(15) =1733a(16) =1877a(17) =1913a(18) =1949a(19) =2273a(20) =2309a(21) =2633a(22) =2777a(23) =3677a(24) =3821a(25) =4397a(26) =4721a(27) =5297a(28) =5333a(29) =5477