projecteuler.net

[Nick Hobson]

In mathematics (and programming), "a or b" means "a or b or both".  This  
is slightly different from standard English usage, where "a or b" can  
often imply "... but not both."  Since projecteuler.net is a mathematical  
programming site, you would expect the mathematical meaning to prevail;  
that is, "multiples of 3 or 5" includes multiples of 3 *and* 5; i.e.,  
multiples of 15.  If you register and submit an answer, you'll find that  
that is indeed what is expected!

Nick


On Tue, 13 Mar 2007 11:16:17 -0000, Zakir Seidov <zakseidov at gmail.com>  
wrote:

> Sorry, "excluded" not "excuded", Zak
>
> On 3/13/07, Zakir Seidov <zakseidov at gmail.com> wrote:
>> Nick, seqfans,
>>
>> Should we start again those contra-productive endless boring discussions
>> which sequences are (or not)  worth for OEIS?
>> I don't think we should,
>> thanks to you all, Zak
>>
>> Nick,
>> multiples of 15 are excluded by definition,
>> in Problem 1.
>>
>> On 3/13/07, Nick Hobson <nickh at qbyte.org> wrote:
>> > Zak,
>> >
>> > Why exclude multiples of 15?  A multiple of 15 is a multiple of 3 or  
>> 5.
>> >
>> > Also, do you think this sequence is really a good candidate for  
>> inclusion
>> > in OEIS?  It seems a little arbitrary to me.  If this sequence is
>> > included, why not similar sequences based on multiples of 2 or 3 (Cf.
>> > A047229), 2 or 5, 2 or 7, 3 or 7, 5 or 7, 2 or 3 or 5, and so on?
>> >
>> > Nick
>> >
>> >
>> > On Tue, 13 Mar 2007 09:21:59 -0000, Zakir Seidov <zakseidov at gmail.com>
>> > wrote:
>> >
>> > > Max, seqfans,
>> > > This is my solution of Problem 1,
>> > > Thanks, Zak
>> > >
>> > > %I A000001
>> > >
>> > > %S A000001
>> > >  
>> 0,0,3,3,8,14,14,14,23,33,33,45,45,45,45,45,45,63,63,83,104,104,104,128,153,153,180,180,180,180,180,180,213,213,248,284,284,284,323,363,363,405,405,405,405,405,405,453,453,503,554,554,554,608,663,663,720,720,720,720,720,720,783,783,848,914,914,914,983,1053,1053,1125,1125,1125,1125,1125,1125,1203,1203,1283,1364,1364,1364,1448,1533,1533,1620,1620,1620,1620,1620,1620,1713,1713,1808,1904,1904,1904,2003,2103
>> > > %N A000001 Sum of numbers <=n which are multiples of 3 or 5 but  
>> not
>> > > 15.
>> > > %C A000001 Sum of numbers m<=n such that mod(m,3)*mod(m,5)=0 and
>> > > mod(m,15)>0.
>> > > First differences (fd) are
>> > > 0,3,0,5,6,0,0,9,10,0,12,0,0,0,0,
>> > > 0,18,0,20,21,0,0,24,25,0,27,0,0,0,0,
>> > > 0,33,0,35,36,0,0,39,40,0,42,0,0,0,0,...
>> > > fd(1..15)={0,3,0,5,6,0,0,9,10,0,12,0,0,0,0}; for n>15
>> > > fd(n)=fd(n-15)+15 if fd(n-15)>0, fd(n)=0 otherwise.
>> > >
>> > > See problem 1 in Project Euler.
>> > > %H A000001 Author?,<a href="http://projecteuler.net">Project
>> > > Euler.</a>
>> > >
>> > > %F A000001 an[n,d]=d*Floor[n/d];sn[n,d]=(an[n,d]*(an[n,d]  
>> + d))/(2*d);
>> > > a(n)=sn[n,3]+sn[n,5]-2*sn[n,15].
>> > > %t A000001 an[n_,d_]:=d*Floor[n/d];sn[n_,d_]:=(an[n,d]*(an[n,d]
>> > > + d))/(2*d);
>> > > Table[sn[n,3]+sn[n,5]-2*sn[n,15],{n,1000}]
>> > > %O A000001 1
>> > > %K A000001 ,nonn,
>> > > %A A000001 Zak Seidov (zakseidov at gmail.com), Mar 13 2007
>> > >
>> > >
>> > > On 3/13/07, 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
>> > >>
>> > >
>> >
>> >
>> >
>>
>