cp's OEIS Frontend

Home primes of integers greater than 1 are derived by concatenation in nondecreasing order (in base 10 unless otherwise noted) of the prime factors including repeats, and iterating this procedure until a prime is reached.

The percentages of such composites among the total numbers of composites, to 3 significant digits, are 0, 1.45, 3.17, 2.44, 1.78, 1.33, 1.03, 0.844, 0.696 and 0.589, while the percentages of these numbers that are semiprimes that reach a prime in 1 step are (after the undefined 0/0) 100, 87.5, 76.3, 74.0, 71.6, 70.0, 67.9, 66.7 and 65.4. - James G. Merickel, Jun 28 2015

As n increases, this sequence should tend asymptotically toward the number of such composites restricted to those that also reach a homeprime in one iteration (a proper subset of itself). And note also that a value that meets the criterion cannot be divisible by a number that does not, like the 1-digit composites. - James G. Merickel, Jun 28 2015