IMO Shortlist 1978 problem 9
Dodao/la:
arhiva2. travnja 2012. Let
![0<f(1)<f(2)<f(3)<\ldots](/media/m/e/5/1/e5130e3ccc911623fdc701b1f38c5e63.png)
a sequence with all its terms positive
![.](/media/m/b/d/d/bdd5ec3ff70fef87f72128d28ab734d1.png)
The
![n-th](/media/m/b/e/5/be5943460a05e443b4598e683ab0cb52.png)
positive integer which doesn't belong to the sequence is
![f(f(n))+1.](/media/m/8/a/8/8a8f01c93b589a2a44b7cbdcf25dc889.png)
Find
%V0
Let $0<f(1)<f(2)<f(3)<\ldots$ a sequence with all its terms positive$.$ The $n-th$ positive integer which doesn't belong to the sequence is $f(f(n))+1.$ Find $f(240).$
Izvor: Međunarodna matematička olimpijada, shortlist 1978