+
+=
++=
+=
++++=
+===+=
++++++=
+=
++=
+=+===+=+=
++++++++++=
+===+=

Explain the pattern and find the next five rows.

Hint: the symbols I chose have nothing to do with the pattern.

The below formula might seem complicated but actually it isn't!
It is presented as an algorithm,whereas "s" is the sequence number and "x" is the position(number) of each element in the sequence.

The first element is always +
Now the loop :

>For x=2 to s do

>If x a prime :
> If (s)modulo(x)=0 then
> we have a "="
> If s is a power of x then exit loop
> Else we have a "+"
>If x not a prime :
> If any of the factors of x has a "=" then
> we have a "="
> If (s)modulo(x)=0 then exit loop
> Else we have a "+"

The 17 first sequences :

1) +
2) +=
3) ++=
4) +=
5) ++++=
6) +===+=
7) ++++++=
8) +=
9) ++=
10) +=+===+=+=
11) ++++++++++=
12) +===+=
13) ++++++++++++=
14) +=+=+===+=+=+=
15) ++=+==++==+=++=
16) +=
17) ++++++++++++++++=

I was too lazy to test it for all the sequences so I'm not 100% sure...

Posted by es_rever on 2004-02-20 22:16:32