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 A259747 #27 Apr 30 2020 18:57:58
%S A259747 1,111,1112111,111211131112111,1112111311121114111211131112111,
%T A259747 111211131112111411121113111211151112111311121114111211131112111
%N A259747 a(0) = 1; thereafter a(n) is the concatenation of a(n-1), n, a(n-1).
%F A259747 a(1)=1 and a(n) = a(n - 1)*10^(2^n) + n *10^(2^n - 1) + a(n - 1).
%t A259747 concatPal[0] = 1; concatPal[n_] := FromDigits @ Join[RealDigits[concatPal[n - 1]][[1]], {n}, RealDigits[concatPal[n - 1]][[1]]]; Table[concatPal[n], {n, 0, 10}]
%t A259747 nxt[{n_,a_}]:={n+1,FromDigits[Flatten[Join[IntegerDigits[a], IntegerDigits[ n+1], IntegerDigits[ a]]]]}; NestList[nxt,{0,1},5][[All,2]] (* _Harvey P. Dale_, Apr 30 2020 *)
%o A259747 (PARI) main(size) = {s=vector(size); s[1]=1; for(t=2,size,s[t]= eval(Str(s[t-1],t-1,s[t-1]))); return(s);} \\ _Anders Hellström_, Jul 05 2015
%Y A259747 Cf. A001704, A007908.
%K A259747 nonn,base
%O A259747 0,2
%A A259747 _José María Grau Ribas_, Jul 04 2015