Palindromic Triangular Numbers with Palindromic Index
Jump to navigation
Jump to search
Sequence
The palindromic triangular numbers whose indices are themselves palindromic are:
| \(\ds T_1\) | \(=\) | \(\ds 1\) | ||||||||||||
| \(\ds T_2\) | \(=\) | \(\ds 3\) | ||||||||||||
| \(\ds T_3\) | \(=\) | \(\ds 6\) | ||||||||||||
| \(\ds T_{11}\) | \(=\) | \(\ds 66\) | ||||||||||||
| \(\ds T_{77}\) | \(=\) | \(\ds 3003\) | ||||||||||||
| \(\ds T_{363}\) | \(=\) | \(\ds 66 \, 066\) | ||||||||||||
| \(\ds T_{1111}\) | \(=\) | \(\ds 617 \, 716\) | ||||||||||||
| \(\ds T_{2662}\) | \(=\) | \(\ds 3 \, 544 \, 453\) | ||||||||||||
| \(\ds T_{111 \, 111}\) | \(=\) | \(\ds 6 \, 172 \, 882 \, 716\) | ||||||||||||
| \(\ds T_{246 \, 642}\) | \(=\) | \(\ds 30 \, 416 \, 261 \, 403\) | ||||||||||||
| \(\ds T_{11 \, 111 \, 111}\) | \(=\) | \(\ds 61 \, 728 \, 399 \, 382 \, 716\) | ||||||||||||
| \(\ds T_{363 \, 474 \, 363}\) | \(=\) | \(\ds 66 \, 056 \, 806 \, 460 \, 865 \, 066\) | ||||||||||||
| \(\ds T_{2 \, 664 \, 444 \, 662}\) | \(=\) | \(\ds 3 \, 549 \, 632 \, 679 \, 762 \, 369 \, 453\) | ||||||||||||
| \(\ds T_{26 \, 644 \, 444 \, 662}\) | \(=\) | \(\ds 354 \, 963 \, 215 \, 686 \, 512 \, 369 \, 453\) | ||||||||||||
| \(\ds T_{246 \, 644 \, 446 \, 642}\) | \(=\) | \(\ds 30 \, 416 \, 741 \, 529 \, 792 \, 514 \, 761 \, 403\) | ||||||||||||
| \(\ds T_{266 \, 444 \, 444 \, 662}\) | \(=\) | \(\ds 35 \, 496 \, 321 \, 045 \, 754 \, 012 \, 369 \, 453\) | ||||||||||||
| \(\ds T_{2 \, 466 \, 444 \, 446 \, 642}\) | \(=\) | \(\ds 3 \, 041 \, 674 \, 104 \, 186 \, 814 \, 014 \, 761 \, 403\) | ||||||||||||
| \(\ds T_{3 \, 654 \, 345 \, 456 \, 545 \, 434 \, 563}\) | \(=\) | \(\ds 6 \, 677 \, 120 \, 357 \, 887 \, 130 \, 286 \, 820 \, 317 \, 887 \, 530 \, 217 \, 766\) |
The sequence of the index elements is A008510 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
The sequence of the triangular elements is A229236 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Historical Note
David Wells reports in Curious and Interesting Numbers, 2nd ed. that Charles Ashbacher reports on this sequence (in particular $363 \, 474 \, 363$) in Journal of Recreational Mathematics, Volume $24$, page $184$, but this has not been corroborated.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $363,474,363$