[seqfan] Re: A154296: primes in A002381 ?

[Maximilian Hasler]

On Mon, Dec 31, 2012 at 4:27 AM, юрий герасимов <2stepan at rambler.ru> wrote:
>
> (3, 7, 29, 31) = A154296 = primes of the form:
> 1/x + 2/x + 3/x + 4/x + 5/x + 6/x + 7/x..., x = 15.


I noticed that there are several sequences with such a name,

1/x + 2/x + 3/x + 4/x + 5/x + 6/x + 7/x..., x = (something)

I think this is confusing. It appears as if one would sum fractions,
but actually it is

(1+2+....)/15

or as Richard Mathar wrote,

(a triangular number)/15.

This makes the nature of these sets of numbers much more
evident than the "mysterious sum of fractions".

It is also clear from this expression
that there are no other primes of that form --
given that T(n) = n(n+1)/2, when n>2*3*5, then T(n)/15
can "at best" be a semiprime because of the two factors
in the numerator which cannot be cancelled by de denominator.

I think authors should make an effort
to use the simplest possible definitions,
and add possible "curious" interpretations as comment,
if desired.


To close, let me present my slightly late, but nonetheless very best
wishes for baktun 13, to all Sequence Fanatics !

Maximilian