# Formula for Sequence of Rational Numbers

I am trying to find a formula for the $n$th term of a sequence of rational numbers less than 1. Regardless of how many terms I include in the table, FindSequenceFunction copies the input as the output. Perhaps my sequence is too complicated, but I would like to know if there are any other methods or functions which help find the $n$th term of a sequence.

Here's the code for the sorted table:

sopf[n_] := Plus @@ (First /@ FactorInteger[n])
Composite[n_Integer] := FixedPoint[n + PrimePi[#] + 1 &, n]
Sort[Table[
1 - ((1 + sopf[Composite[j]] - PrimeNu[Composite[j]])/
Composite[j]), {j, 1, 30}]]


With output

*{1/3, 2/5, 3/7, 5/11, 6/13, 8/17, 9/19, 1/2, 8/15, 4/7, 20/33, 8/13,
2/3, 2/3, 24/35, 7/10, 5/7, 8/11, 11/15, 3/4, 16/21, 7/9, 4/5, 5/6,
38/45, 17/20, 7/8, 8/9, 8/9, 15/16}*

• try oeis.org perhaps Oct 21 '17 at 22:00
• @pdmclean that only works for integers. Oct 21 '17 at 22:26
• Yes, but you can search the sequence of numerators and the sequence of denominators separately. Oct 26 '17 at 13:11
• I tried, they didn't match any sequence in their database. Oct 27 '17 at 1:58

a = Sort[RandomInteger[{1, 100}, 20]];