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 A068664 #14 Oct 26 2019 02:07:02
%S A068664 1,2,4,8,88,616,6776,88088,616616,232464232,21154245112,232696696232,
%T A068664 21175399357112,21154245133154245112,232696696464696696232,
%U A068664 21175399378287399357112,63386501441764911946714410568336
%N A068664 a(1) = 1, a(n) = smallest palindromic multiple of a(n-1).
%t A068664 a=1; Print[a]; For[n = 2, n <= 15, n++, {an = a; k = 2; str = ToString[k*an]; rstr = StringReverse[str]; While[str != rstr, {k = k + 1; str = ToString[k*an]; rstr = StringReverse[str]; If[k*an > 10^20, {Print["Too big"]; Abort[]}]}]; a := k*an; Print[k, " ", a];}]
%t A068664 spm[n_]:=Module[{k=2},While[!PalindromeQ[k*n],k++];k*n]; NestList[spm,1,15] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 02 2019 *)
%Y A068664 A068667 (from a(3) on) and this sequence (from a(6) on) coincide.
%Y A068664 Cf. A068665, A068666, A068667, A068668, A070069, A068971, A068972, A068973, A068974.
%K A068664 base,nonn
%O A068664 1,2
%A A068664 _Amarnath Murthy_, Mar 01 2002
%E A068664 Extended and edited by _John W. Layman_, Mar 18 2002
%E A068664 Last two terms from _David W. Wilson_ and _Patrick De Geest_, Mar 30 2002