Non-Palindromes in Base 2 by Reverse-and-Add Process/Historical Note

Historical Note on Non-Palindromes in Base 2 by Reverse-and-Add Process

This result, according to David Wells in his $1986$ book Curious and Interesting Numbers, was given by Roland Sprague, but the source for this has not been identified.

Independently of Sprague's work, Glyn Johns and James Wiegold, in the context of a children's mathematics club in Cardiff, Wales, noted the reverse-and-add behaviour of $1010100_2$.

Their subsequent report in Volume $78$, issue $483$ of The Mathematical Gazette was used as the basis of the analysis given here in $\mathsf{Pr} \infty \mathsf{fWiki}$, but it needs to be pointed out that there are a number of mistakes in that source.

Sources

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