Probably finite sequence. The multiplicative persistence of a number is the number of times you need to multiply the digits together before reaching a single digit.
Table of n, a(n) for n=0..11.
For n=4, a(4) = 39 because 39 is the smallest nonprime number with multiplicative persistence 3: 39 -> 27 -> 14 -> 4.
Cf. A046500 (smallest prime with multiplicative persistence n).
Sequence in context: A087473 A014120 A003001 * A038350 A003344 A047721
Adjacent sequences: A198374 A198375 A198376 * A198378 A198379 A198380
Jaroslav Krizek, Oct 23 2011