# projecteuler.net

Nick Hobson nickh at qbyte.org
Tue Mar 13 11:14:08 CET 2007

```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
>>
>

```