Take A000040, omit commas: 23571113171923..., select 5-digit primes seen when scanning from left.

Terms

a(0) =11131a(1) =11317a(2) =13171a(3) =23293a(4) =74143a(5) =14347a(6) =96167a(7) =98389a(8) =71011a(9) =1103a(10) =7109a(11) =13127a(12) =31271a(13) =12713a(14) =37139a(15) =51157a(16) =57163a(17) =17317a(18) =79181a(19) =91811a(20) =18119a(21) =91193a(22) =19319a(23) =23227a(24) =39241a(25) =51257a(26) =26927a(27) =27127a(28) =81283a(29) =32933