a(n) = min{k>0: the n-th convergent to e equals m/k! for some m}.

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =7a(5) =8a(6) =13a(7) =71a(8) =31a(9) =67a(10) =13a(11) =89a(12) =83a(13) =18089a(14) =5441a(15) =17377a(16) =36269a(17) =26021a(18) =4909a(19) =10391023a(20) =1097a(21) =28879a(22) =1846921a(23) =519691a(24) =1329313a(25) =793279a(26) =7553783a(27) =3308341a(28) =65676881a(29) =662407