projecteuler.net

[Nick Hobson]

I should state upfront my interest: I have recently become a member of the  
Project Euler team; I help to devise and select problems.

One of the issues we face as problem designers is that of contestants  
simply looking up the answer in OEIS!  Of course, this is partly what OEIS  
is for.  Also, someone who simply looks up an answer, rather than trying  
to work it out for themselves, is missing out on the process of discovery.

Then there is a sort of middle ground, where a brute-force solution of the  
actual problem is impossible, but brute-force can be used to determine the  
first few terms of a sequence, which can then be looked up in OEIS.  My  
own feeling (and that of at least some of the other team members) is that  
this is simply making good use of the tools available.  Of course, to get  
the most out of the problem, having obtained the answer, a contestant  
should then go back and try to design and code a solution themselves.

I'm not about to ask people not to submit Project Euler-related  
sequences.  That would not only be fruitless, but it would go against the  
ethos of OEIS, and the open nature of information flow on the Internet.   
If you submit a sequence from Project Euler, I ask only that, if at all  
possible, please do not include enough terms to directly give away the  
answer.  Sometimes that's quite easy to manage; see several examples  
below.  Other times, it would be impossible to add the sequence without  
giving away the answer.  In either case, I say: thank you for submitting  
the sequence!

I have submitted a small number of Project Euler-related sequences, but in  
each case I've refrained from extending the sequence far enough to give a  
direct answer to a problem, and from giving a program that clearly shows  
the logic required to solve the problem.

For instance, A126255 corresponds to Project Euler problem 29; a(100)  
(which is not listed) is the answer to the problem.  I deliberately did  
not send a b-file for this sequence (which would have included a(100)),  
while the PARI/GP script presented is relatively obscure and inefficient,  
and relies upon a 'big integer' library to work at all.  By contrast, I  
did provide a b-file for the very similar (and canonical?) sequence  
A126254.

A similar example is A127629, where the sequence as given does not extend  
far enough to answer the Project Euler problem (number 141), and the  
PARI/GP function shown is unsuitable for solving the problem.

In fact, I believe the above two examples are the only Project Euler  
sequences I've submitted, though a few others are related.  For instance,  
A126086 represents a generalisation (and then extension to three  
dimensions) of problem 15.  Similarly, A126130 was inspired by problem  
101, but is sufficiently different that I thought it unnecessary to list  
Project Euler in the links.

Then there are Project Euler-related sequences that I've considered  
submitting to OEIS, but rejected, because they are of no mathematical  
significance.

An example is problem 109: How many distinct ways can a player checkout in  
the game of darts with a score of less than 100?  Obviously, this can be  
made into a finite sequence, of which a(100) (or maybe a(99)) is the  
answer to the problem.  However, it seems to me this sequence would have  
no mathematical significance.  I'm aware that one of Neil's goals for OEIS  
is for it to list solutions to published problems, but in this case I  
thought omission was the better part of valour!

Nick


On Tue, 13 Mar 2007 03:55:03 -0000, Max Alekseyev <maxale at gmail.com> wrote:

> SeqFans,
>
> http://projecteuler.net provides quite long list of challenging
> computational-math problems. I wonder if solutions to these problems
> are present in OEIS. If not, it may be a good source for new
> sequences. Can anybody check that out?
>
> Thanks,
> Max
>





"Max Alekseyev" <maxale at gmail.com> wrote:
:SeqFans,
:
:http://projecteuler.net provides quite long list of challenging
:computational-math problems. I wonder if solutions to these problems
:are present in OEIS. If not, it may be a good source for new
:sequences. Can anybody check that out?

I have code to solve many of the problems, but I don't have time to trawl
through them for possible sequences right now. If there are specific ones
that look likely to be interesting, please nudge me to dig out the code
I have.

There is one series of problems (##81-83) that triggered an indirectly
related sequence that I have still to write up: counting how many paths
which is the number of, er, "very-self-avoiding paths" on a rectangular
lattice - paths that do not loop back to traverse a node adjacent to one
traversed earlier. (This can also be made more generic, both by varying
the dimensions of the lattice, and by varying the minimum gap between
nodes.)

Hugo




Dear Seqfans, the following was submitted by an anonymous 
correspondent - well, someone who so far has not responded
to my email asking for more information.

The question is, what is the definition?  I guess it is supposed 
to be apparent from the %N line.

Thanks

Neil


%I A000001
%S A000001 1 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 0 1 1 1 0 1
%N A000001 Binary splitting
%e A000001 ~
%O A000001 1
%K A000001 ,nonn,
%A A000001 KlangenFarben (klangenfarben at gmail.com), Mar 11 2007