Formula that captivated Ramanujan found

For instance,4 = 31 = 22 = 211 = 1111,so the partition number of 4 is 5. However,it becomes more complex with larger numbers and many mathematicians have struggled to find a formula for calculating it.

Ramanujan developed an approximate formula in 1918,which helped him spot that numbers ending in 4 or 9 have a partition number divisible by 5,and he found similar rules for partition numbers divisible by 7 and 11.

He offered no proof but said that these numbers had 8220;simple properties8221; possessed by no others.

Now Ken Ono at Emory University in Atlanta,Georgia,and his colleagues have developed a formula that spits out the partition number of any integer.

They found 8220;fractal8221; relationships in sequences of partition numbers of integers that were generated using a formula containing a prime number.

For instance,in a sequence generated from 13,all the partition numbers are divisible by 13,but zoom in and you will find a sub-sequence of numbers that are divisible by 132,a further sequence divisible by 133 and so on.

Ramanujan8217;s numbers are the only ones with no fractal behaviour at all. That may be what he meant by simple properties,says Ono.

8220;It8217;s a privilege to explain Ramanujan8217;s work. It8217;s something you8217;d never expect to be able to do, New Scientist quoted Ono as saying.