A self-"read and extend" sequence built following the rules visible in the Comments section.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =16a(5) =32a(6) =46a(7) =92a(8) =841a(9) =1268a(10) =2356a(11) =1247a(12) =9442a(13) =14888a(14) =97762a(15) =955421a(16) =1910842a(17) =1234688a(18) =2346679a(19) =3345689a(20) =9876631a(21) =12235679a(22) =12344578a(23) =12456689a(24) =98743321a(25) =124466789a(26) =233457889a(27) =145667789a(28) =123355789a(29) =877654211