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%I #9 Apr 27 2019 20:36:47
%S 3,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of palindromic hexagonal numbers of length n whose index is also palindromic.
%C Is there a nonzero term beyond a(7)?
%H P. De Geest, <a href="http://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 hexagonal number of length 4 whose index is also palindromic, 55->5995. Thus, a(4)=1.
%t A054969 = {0, 1, 6, 66, 3003, 5995, 15051, 66066, 617716, 828828, 1269621, 1680861, 5073705, 5676765, 1264114621, 5289009825, 6172882716, 13953435931, 1313207023131, 5250178710525, 6874200024786, 61728399382716, 602224464422206, 636188414881636, 1250444114440521, 16588189498188561, 58183932923938185, 66056806460865066, 67898244444289876, 514816979979618415, 3075488771778845703, 6364000440440004636, 15199896744769899151};
%t A054970 = {0, 1, 2, 6, 39, 55, 87, 182, 556, 644, 797, 917, 1593, 1685, 25141, 51425, 55556, 83527, 810311, 1620213, 1853942, 5555556, 17352586, 17835196, 25004441, 91071921, 170563673, 181737182, 184252876, 507354403, 1240058219, 1783816196, 2756800387};
%t Table[Length[ Select[A054970[[Table[ Select[Range[18], IntegerLength[A054969[[#]]] == n || (n == 1 && A054969[[#]] == 0) &], {n, 19}][[n]]]], PalindromeQ[#] &]], {n, 19}]
%Y Cf. A000384, A054969, A054970, A082721, A307717, A307752, A307753.
%K nonn,base,hard,more
%O 1,1
%A _Robert Price_, Apr 27 2019
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