Tuesday 16 June 2015 — This is over nine years old. Be careful.
53 is a hex-palindrome: 5310 = 3516, or in programming terminology: 53 == 0x35.
In fact, the only numbers with this property (other than the trivial single-digit numbers) are multiples of 53:
| 53 = | 3516 | = 53 × 1 |
| 371 = | 17316 | = 53 × 7 |
| 5141 = | 141516 | = 53 × 97 |
| 99481 = | 1849916 | = 53 × 1877 |
| 8520280 = | 082025816 | = 53 × 160760 |
Update: I asked for a proof of this on math.stackexchange.com, and I got one!
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