Concatenating the proper divisors of a number
If you string together all the prime factors of a number, and repeat, stopping
when you reach a prime, you get the classic sequence of
home primes, A037274 (where
the 49th term is still unknown after all these years--see
Eric Angelini recently suggested stringing together all the
proper divisors of the number, that is,
all divisors except 1 and the number itself.
A120712 is the first of these new entries:
it gives numbers n such that the concatenation of the proper divisors of n
is a prime.
But look at A120716: start
at n and repeatedly concatenate
the proper divisors until you reach a prime, setting the value
to -1 if we never reach a prime.
For example, the proper divisors of 6 are 2 and 3, so 6 -> 23,
and since 23 is a prime, a(6) = 23. The big question is,
what is a(8)? The
beginning of the trajectory of 8 can
be found here.
There is a very large number that needs to be factored!
At lunch the other day we came up with four variants of
hoping to find one where we could compute more terms:
But in every case we quickly get stopped.
A pessimist might say that the human race will
never find the next term in any of the last five sequences
It would be nice to know more! [Aug 02 2007]