A307850 Number of palindromic triangular numbers of length n whose index is also palindromic.
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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
Examples
There is only one palindromic triangular number of length 2 whose index is also palindromic. 11->66. Thus, a(2)=1.
Links
- Patrick De Geest, Palindromic Squares in bases 2 to 17
- Eric Weisstein's World of Mathematics, Palindromic Number
Programs
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Mathematica
A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ] (* Set Range to level of desired running time. *) A008509 = Select[Range[0, 10^6], PalindromeQ[PolygonalNumber[3, #]] &] (* Set Range to level of desired running time. *) Table[Length[ Select[A008509[[Table[ Select[Range[35], IntegerLength[A003098[[#]]] == n || (n == 1 && A003098[[#]] == 0) &], {35}][[n]]]], PalindromeQ[#] &]], {n, 11}] (* 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. *)