# projecteuler.net

Zakir Seidov zakseidov at gmail.com
Tue Mar 13 12:16:17 CET 2007

```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
> > >>
> > >
> >
> >
> >
>

```