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Does the following help (if not, ask for more) ?

sage: for beta in srange(0.91,0.99,0.02):
....:     print n-beta*n-1
....:     
89.0000000000000
69.0000000000000
48.9999999999999
28.9999999999999

a numerical noise that can be fixed as follows:

sage: for beta in srange(0.91,0.99,0.02):
....:     print round(n-beta*n-1)
89
69
49
29