A135485 and primes (and emirps) in A135485; New Prime Curio about 15013 by Post

[Jonathan Post]

To: editor
Subject: New Prime Curio about 15013 by Post
From: Prime Curios! automailer for <jvospost3 at gmail.com>
http://primes.utm.edu/curios/

There has been a new curio submitted for your approval:

15013 [number_id=7550]

2^0 + 3^1 + 5^2 + 7^3 + 11^4 = 15013 = Sum_{i=1..5) p(i)^(i-1), where
p(i) denotes i-th prime number, is the largest known such prime (as of
13 Feb 2008) and, curiously, the smallest emirp of that form.

Reference:
A135485 Sum_{i=1..n) p(i)^(i-1), where p(i) denotes i-th prime number.

[Post]



Hopefully this idea isn't too esoteric or innane for the list, it's
oracle with the following property -- it could tell you what happened when
you add 1 to an integer. What are all of the "observables" (and I mean that
in a quasi-quantum physics sense) that the oracle would describe? My first
thought is that there are an infinite number of observable properties for
any integer. However, does the number of "observables" go up with the size
of any particular integer (both in the positive and negative directions)? If
be nailed down; so much seems to depend on how you define "observables" and
it seems like one could invent an arbitrary number of properties for any
particular integer or set of integers.







Dear Seqfans, Patrick A. Kirol submitted a sequence
which I did not understand.  After reading his reply, 
I think that the problem can be stated as follows:

Find the shortest (and lexicographically earliest)
decimal string which contains all the 2-digit strings 01, 02,
..., 98, 99.

Presumably something like this will be optimal:

1 0 1 1 2 1 3 ... 9 9

Here is what he sent me:

%S A000001 0,01,02,03,04,05,06,07,08,09,1,12,13,14,15,16,17,18,19,2,23,24,25,26,27,28,29,3,34,35,36,37,38,39,4,45,46,47,48,49,5,56,57,58,59,6,67,68,69,7,78,79,8,89,9

but I think the version in the
OEIS should be a string of single digits seperated by commas.
The string /could/ begin with 0, but it's not obvious that that
is optimal.

Neil