Fusible Numbers I
C_K_Yang liuguangxi madbat2 C3PO Philippe_57721 gerrob mathpseudo sinan hervas clytorock dloser nielkh
Public  02/27/15  6xp  Programming  44.8% 
Fusible numbers are an extraordinary set of rational numbers. You can learn more here.
There are defined by the following rules:
Find all fusible numbers in the interval ] 1/2 , 5/4 [ (bounds excluded) with a denominator ≤ 128
Answer format : comma separated list in ascending order
(We represent a fusible number p/2^q as p.q. E.g: 3/4 = 3.2)
Example : 15.4,63.6,1.0,5.1
[My timing: < 1 sec]
There are defined by the following rules:
 We define the operation ~ between 2 reals as a ~ b = (a + b + 1)/2
 0 is a fusible number
 c is a fusible number is there exist fusible numbers a & b such as c = a ~ b AND a  b < 1
1/2 = 0~0 1 = (0~0)~(0~0) 5/4 = (0~0)~((0~0)~(0~0))It is easy to see that all fusible numbers other than 0 can be written p/2^q for some integers p & q where p is odd.
Find all fusible numbers in the interval ] 1/2 , 5/4 [ (bounds excluded) with a denominator ≤ 128
Answer format : comma separated list in ascending order
(We represent a fusible number p/2^q as p.q. E.g: 3/4 = 3.2)
Example : 15.4,63.6,1.0,5.1
[My timing: < 1 sec]
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