3-Digit Numbers forming Longest Reverse-and-Add Sequence/Historical Note

Historical Note on 3-Digit Numbers forming Longest Reverse-and-Add Sequence

David Wells includes the following quote in his Curious and Interesting Numbers, 2nd ed. of $1997$:

The remaining $75$ numbers can be classified into just a few groups, the members of which after one or two reversals each produce the same number and are therefore essentially the same. One of these groups consists of the numbers $187$, $286$, $385$, $583$, $682$, $781$, $869$, $880$ and $968$, each of which when reversed once or twice forms $1837$ and eventually forms the palindromic number $8,813,200,023,188$ after $23$ reversals.

He attributes this quote to Richard Hamilton, but no reference to it can be found on the internet, apart from its appearance in the above source work, and it has not been possible to corroborate it.

Technically speaking, of course, $869$ and $968$ take just $22$ iterations.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $196$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $196$