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%I #23 Aug 11 2024 14:41:34
%S 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 Number of palindromic pentagonal numbers of length n whose index is also palindromic.
%C Is there a nonzero term beyond a(5)?
%H P. De Geest, <a href="https://www.worldofnumbers.com/square.htm">Palindromic Squares</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%e There is only one palindromic pentagonal number of length 4 whose index is also palindromic, 44->2882. Thus, a(4)=1.
%t 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 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 Table[Length[Select[A028386[[Table[Select[Range[18], IntegerLength[A002069[[#]]] == n || (n == 1 && A002069[[#]] == 0) &], {n, 18}][[n]]]], PalindromeQ[#] &]], {n, 18}]
%Y Cf. A000326, A002069, A028386, A059868, A263618, A307717.
%K nonn,base,hard,more
%O 1,1
%A _Robert Price_, Apr 26 2019
%E a(19)-a(35) from _Chai Wah Wu_, Sep 07 2019
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