OFFSET
1,3
COMMENTS
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
LINKS
Wikipedia, Home prime
EXAMPLE
21=3*7 and 37 is prime, and no other composite 2-digit number has a 2-digit home prime; so a(2)=1. Starting with a composite implies at least 2 digits, so a(1)=0 trivially.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
James G. Merickel, Dec 10 2012
EXTENSIONS
a(9) and a(10) added by James G. Merickel, Jun 28 2015
STATUS
approved