Triangular Numbers which are also Square/Sequence

Sequence of Triangular Numbers which are also Square

The sequence of triangular numbers which are also square begins:

$1, 36, 1225, 41 \, 616, 1 \, 413 \, 721, \ldots$

This sequence is A001110 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Their indices are:

$1, 8, 49, 288, 1681, 9800, \ldots$

This sequence is A001108 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Their roots are:

$1, 6, 35, 204, 1189, \ldots$

This sequence is A001109 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $15$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $15$