Identification of fractional sequences

[N. J. A. Sloane]

On 4/23/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> Possible duplicates:
> Will the sequences A068310 and A086485 ever differ? Glancing at the problem
> I think they will at some value for n, but n would probably have to be very
> large. If not, then these are duplicates.

I don't understand.  Their definitions look identical to me!

> On a similar note, A106766 and
> A119892 will probably differ at some point, too. It is kind of interesting
> that they match as well as they do.

Well, the digit sum must be the largest member of a prime trio, so the
first number where the sequences differ must be with digit sum 47, and
thus have at least 6 digits -- so until then you get all the primes
with 4 or 5 digits that have digit sum 29, and that's a lot of terms.
Similarly A119891 has all its entries having digit sum 11 for a long
while until the first 23 comes in.

--Joshua Zucker