Palindromic Triangular Numbers

Sequence of Palindromic Triangular Numbers
The sequence of triangular numbers which are also palindromic begins:
 * $1, 3, 6, 55, 66, 171, 595, 666, 3003, 5995, 8778, 15 \, 051, 66 \, 066, 617 \, 716, 828 \, 828, 1 \, 269 \, 621, 1 \, 680 \, 861, 3 \, 544 \, 453, \ldots$

Their indices are:
 * $1, 2, 3, 10, 11, 18, 34, 36, 77, 109, 132, 173, 363, 1111, 1287, 1593, 1833, 2662, \ldots$