what defines A113495?

Richard Mathar mathar at strw.leidenuniv.nl
Wed Feb 20 19:13:45 CET 2008

sequence of consecutive primes. So my expectation of just taking
    Can we partition the perfect powers A001597 into any sum of 
    1+odd primes to make it into the sequence?
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Date: Wed, 20 Feb 2008 10:57:29 -0800
From: "Max Alekseyev" <maxale at gmail.com>
To: "Richard Mathar" <mathar at strw.leidenuniv.nl>
Subject: Re: what defines A113495?
Cc: seqfan at ext.jussieu.fr
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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.


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

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