%I #18 Oct 19 2023 23:34:23
%S 1,9,10,91,28,54,191,1000,9001,1089,8712,3466,3177,4536,1818,6363,
%T 7273,6454,8092,4816,1368,7263,6364,8272,4456,2088,6714,7462,5185,630,
%U 406,198,693,703,604,802,1278,7443,6004,8002,4006,1998,6993,7003,16004,24057,50985,7920,2377,5355,180
%N a(n), read backwards, is present as a substring in a(n) + a(n+1). This is the lexicographically earliest sequence of distinct terms > 0 with this property.
%e a(1), read backwards, is 1, which is present in a(1) + a(2) = 1+ 9 = 10;
%e a(2), read backwards, is 9, which is present in a(2) + a(3) = 9+10 = 19;
%e a(3), read backwards, is 01, which is present in a(3) + a(4) = 10+91 = 101;
%e a(4), read backwards, is 19, which is present in a(4) + a(5) = 91+28 = 119; etc.
%t a[1]=1;a[n_]:=a[n]=(k=1;While[MemberQ[Array[a,n1],k] !StringContainsQ[ToString[a[n1]+k],StringReverse@ToString@a[n1]],k++];k); Array[a,51]
%o (Python)
%o from itertools import count, islice
%o def agen(): # generator of terms
%o an, aset, mink = 1, set(), 2
%o while True:
%o yield an; aset.add(an); t = str(an)[::1]; mink = max(int(t)an, 2)
%o an = next(k for k in count(mink) if k not in aset and t in str(an+k))
%o print(list(islice(agen(), 51))) # _Michael S. Branicky_, Oct 15 2023
%Y Cf. A004086.
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Giorgos Kalogeropoulos_, Oct 15 2023
