+
+=
++=
+=
++++=
+===+=
++++++=
+=
++=
+=+===+=+=
++++++++++=
+===+=
Explain the pattern and find the next five rows.
Hint: the symbols I chose have nothing to do with the pattern.
1 +
2 +=
3 ++=
4 +=
5 ++++=
6 +===+=
7 ++++++=
8 +=
9 ++=
10 +=+===+=+=
11 ++++++++++=
12 +===+=
Every prime p is represented by p-1 '+'s followed by an '='. Similarily every power of a prime p^n is represented by p-1 '+'s followed by an '='.
6 and 12 also have the same pattern, so I suspect the pattern is based on the prime factors of the number .
I will conjecture:
13 ++++++++++++=
14 ?
15 ?
16 +=
17 ++++++++++++++++=
18 +===+= [same as 6, 12]
19 ++++++++++++++++++=
20 +=+===+=+= [same as 10]
Some thoughts
