1/1, 2/2, 3/3, 4/5, 5/7, 6/11, 7/15, 8/22, 9/30, 10/42..........etc.
For the life of me, I can't seem to find a pattern in the denominators. The numerators are quite obviously the natural counting numbers. I believe we have studied the sequence, but can't seem to remember what it is! Any help or hint would be appreciated. Thanks.
This is my thinking on this sequence!
The numerator is the natural counting number. The denominator is the "partition function", P(n), of that number, or the number of ways you can make up that number, since all the denominators listed are in perfect order of the P(n) sequence.
1 = 1+0 = 1
2 = 2+0, 1+1. = 2
3 = 3+0, 2+ 1, 1+1+1. = 3
4 = 4+0, 3+1, 2+2, 2+1+1, 1+1+1+1. = 5........and so on. So, the next few terms will be:
..............11/56, 12/77, 13/101, 14/135......and quickly escalates to very large denominators.
