This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A018238 #19 Aug 28 2021 00:00:17
%S A018238 1,21,3121,41213121,5121312141213121,61213121412131215121312141213121,
%T A018238 7121312141213121512131214121312161213121412131215121312141213121
%N A018238 Add 1 to leading digit and put in front.
%C A018238 The concatenation of first n terms (if n is small) yields a palindrome: 1, 121, 1213121, etc. - _Amarnath Murthy_, Apr 08 2003
%C A018238 From _M. F. Hasler_, May 05 2008: (Start)
%C A018238 This is not the case from n=10 on: According to the formula in A123121 A082215(10) has an even number of digits, the middle digits being "10". (In a strict sense, e.g. Def. 3 of the first reference there, A082215(9) is the last Zimin word on the alphabet {1,...,9}, though.)
%C A018238 While there is less ambiguity about the definition of A018238(10), it is not clear if A018238(11) should start with "11..." or with "10..." (the largest digit of all subsequent terms being "9"). According to the formula in A123121, a(100) has 3 digits more than a(99), so the first choice seems appropriate and has been adopted for the given PARI code.
%C A018238 However, it corresponds to a modified definition, "a(n) = concatenation of n and all preceding terms". a(3) is the only prime term up to a(14) included. The sequence is (1,0,1,0,1,0,...) (mod 3), at least up to a(20). (End)
%H A018238 M. F. Hasler, <a href="/A018238/b018238.txt">Table of n, a(n) for n=1,...,11</a>.
%o A018238 (PARI) A018238(n,t="")=for(k=2,n,t=Str(t,k-1,t));eval(Str(n,t)) \\ _M. F. Hasler_, May 05 2008
%Y A018238 Cf. A001511, A082215, A123121, A033564.
%K A018238 nonn,base
%O A018238 1,2
%A A018238 _N. J. A. Sloane_, Michael Minic (minic(AT)mtsu.edu)