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 A307850 #12 Feb 16 2025 08:33:55
%S A307850 4,1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A307850 0,0,0,0,0,0,0,0,0,0,0
%N A307850 Number of palindromic triangular numbers of length n whose index is also palindromic.
%H A307850 Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>
%H A307850 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%e A307850 There is only one palindromic triangular number of length 2 whose index is also palindromic. 11->66. Thus, a(2)=1.
%t A307850 A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ]
%t A307850 (* Set Range to level of desired running time. *)
%t A307850 A008509 = Select[Range[0, 10^6], PalindromeQ[PolygonalNumber[3, #]] &]
%t A307850 (* Set Range to level of desired running time. *)
%t A307850 Table[Length[ Select[A008509[[Table[ Select[Range[35], IntegerLength[A003098[[#]]] == n || (n == 1 && A003098[[#]] == 0) &], {35}][[n]]]], PalindromeQ[#] &]], {n, 11}]
%t A307850 (* Set the first two Ranges to encompass the length of A003098 and the last Range to encompass the length of the last value in A003098. *)
%Y A307850 Cf. A000217, A003098, A008509, A307348, A307367.
%K A307850 nonn,base,hard
%O A307850 1,1
%A A307850 _Robert Price_, May 01 2019