Guy, Richard K., Unsolved problems in number theory, third edition, Problem Books in Mathematics, Springer (2004), xviii+437 pp.; B41 "Iterations of $\phi$ and $\sigma$", p. 148: Finucane's iteration of $\phi(n)+1$, the number of steps to a prime, the distribution of the $n$ whose sequences end in a given prime $p$, and whether 5, 8, 10, 12 are the only numbers leading to 5 and 7, 9, 14, 15, 16, 18, 20, 24, 30 the only ones leading to 7. Library home: Guy 2004.