A220296 Number of n-digit composites with n-digit home primes.

0, 1, 24, 194, 1457, 11027, 86978, 716526, 5948091, 50665173

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

Table of n, a(n) for n=1..10.

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

Cf. A037274, A259493.

Sequence in context: A066406 A271432 A042114 * A282286 A123197 A211151

Adjacent sequences: A220293 A220294 A220295 * A220297 A220298 A220299

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