Palindromic Triangular Numbers

Sequence of Palindromic Triangular Numbers

The sequence of triangular numbers which are also palindromic begins:

$1, 3, 6, 55, 66, 171, 595, 666, 3003, 5995, 8778, 15 \, 051, 66 \, 066, 617 \, 716, 828 \, 828, 1 \, 269 \, 621, 1 \, 680 \, 861, 3 \, 544 \, 453, \ldots$

This sequence is A003098 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Their indices are:

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

This sequence is A008509 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Historical Note

David Wells reports in Curious and Interesting Numbers of $1986$ that examples of the palindromic triangular numbers were examined by Charles Wilderman Trigg.

Sources

• 1973: Charles W. Trigg: Palindromic Triangular Numbers (J. Recr. Math. Vol. 6: pp. 146 – 147)
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $15$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $15$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $55$