Well done, Feline.

the 89th element, that is also the answer I have. That numebr is really big (10^(10^40)), so it is not possible to compute the whole number.

As already sugessted by FeLiNe, the easiest wat to compute the first noninteger element, is to do the whole Equation modulo a prime number. starting witrh 3, 5, 7 etc.

If you have a multiprecision tool, you can also calculate it mod 100! (factorial).

There is also a simplification at mathworld (wolfram research) about GĂ¶bel's Sequence (

http://mathworld.wolfram.com/GoebelsSequence.html )

they transform the sequence in a related one, which is the already the sum of all beginning elements.

So

s[n] = n * x[n]

s[n+1] = s[n] + ((s[n]^3) / n^3)

here the modulo operation is not that difficult.

maybe there is a power, where it takes even longer to meet the first noninteger element...