Take A000040, omit commas: 23571113171923..., select 4-digit primes seen when scanning from left.

Terms

a(0) =2357a(1) =3571a(2) =5711a(3) =3137a(4) =7717a(5) =8389a(6) =1103a(7) =1031a(8) =7109a(9) =1091a(10) =911a(11) =2713a(12) =9151a(13) =1511a(14) =1571a(15) =3167a(16) =9181a(17) =1811a(18) =1193a(19) =1931a(20) =9319a(21) =9719a(22) =1223a(23) =7229a(24) =3323a(25) =9241a(26) =7127a(27) =1277a(28) =1283a(29) =8329