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

1,1

Links

Table of n, a(n) for n=1..45.

P. De Geest, Palindromic Squares

Eric Weisstein's World of Mathematics, Palindromic Number

Example

There is only one palindromic triangular number of length 2 whose index is also palindromic. 11->66. Thus, a(2)=1.

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. *)

Crossrefs

Cf. A000217, A003098, A008509, A307348, A307367.

Sequence in context: A213541 A181435 A206774 * A290455 A290460 A334429

Adjacent sequences: A307847 A307848 A307849 * A307851 A307852 A307853

Keyword

nonn,base,hard

Author

Robert Price, May 01 2019

Status

approved