Consider the fraction, n/d, where n and d are positive integers. If nd and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d 8 in ascending order of size, we get:
1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
It can be seen that 2/5 is the fraction immediately to the left of 3/7.By listing the set of reduced proper fractions for d 1,000,000 in ascending order of size, find the numerator of the fraction immediately to the left of 3/7.
My Solution
(defun Euler71(n)
(let ((constnumber (/ 3 7))
(currentnumber 0)
(tempar 0)
(low 0)
(high 0)
(num 0))
(loop for i from 100000 to n
do(progn (setq high (ceiling (* i (/ 3 7))))
(setq low (- high 200))
(loop for j from low to high
do(progn (setq tempar (/ j i))
(if (and (= 1 (gcd i j))
(> tempar currentnumber)
(< tempar constnumber))
(progn (setq currentnumber tempar)
(incf num)))))))
currentnumber))
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