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 A083816 #13 Jun 14 2024 04:12:28
%S A083816 1,11,919,90109,9001009,900010009,90000100009,9000001000009,
%T A083816 900000010000009,90000000100000009,9000000001000000009,
%U A083816 900000000010000000009,90000000000100000000009,9000000000001000000000009,900000000000010000000000009,90000000000000100000000000009,9000000000000001000000000000009
%N A083816 10^n-th palindrome.
%H A083816 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (111,-1110,1000).
%F A083816 From _Chai Wah Wu_, Jun 13 2024: (Start)
%F A083816 a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 4.
%F A083816 G.f.: (-8000*x^4 + 690*x^3 - 808*x^2 + 100*x - 1)/((x - 1)*(10*x - 1)*(100*x - 1)). (End)
%t A083816 NextPalindrome[n_] := Block[{l = Floor[Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]]]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]]]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[Reverse[ IntegerDigits[idfhn]], Mod[l, 2]]]] ]]]]; p = NestList[ NextPalindrome, 1, 10^5]; Table[ p[[10^n]], {n, 0, 5}]
%Y A083816 Cf. A050250, A099280.
%Y A083816 Cf. A103404.
%K A083816 nonn,base
%O A083816 0,2
%A A083816 _Robert G. Wilson v_, Jun 17 2003
%E A083816 More terms from _Ray Chandler_, Jul 23 2003