# what defines A113495?

Richard Mathar mathar at strw.leidenuniv.nl
Wed Feb 20 21:17:20 CET 2008

```First terms seem to be(?):

%S A113495 1,4,9,16,27,64,125,196,12167,28224,68921,
115600

zak

%C A113495 12167 = 23^3, 28224 = 168^2,  68921 = 41^3,
115600 = 340^2.

--- Jack Brennen <jb at brennen.net> wrote:

> Then shouldn't A113495 go like this:
>
>    1, 4, 9, 16, 27, 64, 125, 196, ...
>
> rather than the listed:
>
>    1, 4, 9, 16, 27, 64, 125, 256, ...
>
>
> ???
>
> After all, 196-125=71 is a prime smaller than
> 256-125=131.
>
>
>
> Max Alekseyev wrote:
> > Richard,
> >
> > I've got an impression that A113495 corresponds to
> a sequence of 1
> > followed by odd primes:
> > P: 1 < p1 < p2 < p3 < ...
> > such that all partial sums of this sequence are
> perfect powers and
> > each of the primes is the smallest possible
> (hence, the sequence P can
> > be viewed as lexicographically smallest of this
> type). The sequence
> > A113495 is simply the partial sums of P.
> >
> > In other words, A113495 is the lexicographically
> smallest subsequence
> > of A001597, such that the sequence of first
> differences of A113495 is
> > a subsequence of A000040.
> >
> > Regards,
> > Max
> >
> > On Wed, Feb 20, 2008 at 10:13 AM, Richard Mathar
> > <mathar at strw.leidenuniv.nl> wrote:
> >>  A113495 is defined as 1 plus the sum of some
> first k
> >>  odd primes, if the sum equals a perfect power.
> The examples
> >>  for a(6)-a(8) seem to indicate that this is not
> to be taken
> >>  literally, because 11, 37, 67, 131 are certainly
> not a
> >>  sequence of consecutive primes. So my
> expectation of just taking
> >>  all A001597(i)=1+A071148(j), which are very few
> as it seems, fails.
> >>
> >>  - is this defined more liberally? How?
> >>     Can we partition the perfect powers A001597
> into any sum of
> >>     1+odd primes to make it into the sequence?
> >>  - is this a modified version of A110997 ?
> >>  - how does this affect A113759 ?
> >>
> >>  Richard
> >>
> >
> >
>
>

____________________________________________________________________________________
Be a better friend, newshound, and
know-it-all with Yahoo! Mobile.  Try it now.  http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ

```