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 A307753 #26 Feb 16 2025 08:33:55
%S A307753 3,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A307753 Number of palindromic pentagonal numbers of length n whose index is also palindromic.
%C A307753 Is there a nonzero term beyond a(5)?
%H A307753 Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>
%H A307753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%e A307753 There is only one palindromic pentagonal number of length 4 whose index is also palindromic, 44->2882. Thus, a(4)=1.
%t A307753 A002069 = {0, 1, 5, 22, 1001, 2882, 15251, 720027, 7081807, 7451547, 26811862, 54177145, 1050660501, 1085885801, 1528888251, 2911771192, 2376574756732, 5792526252975, 5875432345785, 10810300301801, 264571020175462, 5292834004382925, 10808388588380801, 15017579397571051, 76318361016381367, 150621384483126051, 735960334433069537, 1003806742476083001, 1087959810189597801, 2716280733370826172};
%t A307753 A028386 = {0, 1, 2, 4, 26, 44, 101, 693, 2173, 2229, 4228, 6010, 26466, 26906, 31926, 44059, 1258723, 1965117, 1979130, 2684561, 13280839, 59401650, 84885761, 100058581, 225563533, 316882086, 700457153, 818049201, 851649306, 1345679688};
%t A307753 Table[Length[Select[A028386[[Table[Select[Range[18], IntegerLength[A002069[[#]]] == n || (n == 1 && A002069[[#]] == 0) &], {n, 18}][[n]]]], PalindromeQ[#] &]], {n, 18}]
%Y A307753 Cf. A000326, A002069, A028386, A059868, A263618, A307717.
%K A307753 nonn,base,hard,more
%O A307753 1,1
%A A307753 _Robert Price_, Apr 26 2019
%E A307753 a(19)-a(35) from _Chai Wah Wu_, Sep 07 2019