This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A220296 #27 Dec 12 2015 15:41:15 %S A220296 0,1,24,194,1457,11027,86978,716526,5948091,50665173 %N A220296 Number of n-digit composites with n-digit home primes. %C A220296 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. %C A220296 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 %C A220296 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 %H A220296 Wikipedia, <a href="http://en.wikipedia.org/wiki/Home_prime">Home prime</a> %e A220296 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. %Y A220296 Cf. A037274, A259493. %K A220296 nonn,base %O A220296 1,3 %A A220296 _James G. Merickel_, Dec 10 2012 %E A220296 a(9) and a(10) added by _James G. Merickel_, Jun 28 2015