54 lines
1.3 KiB
Factor
54 lines
1.3 KiB
Factor
! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.functions math.primes math.ranges
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sequences project-euler.common math.bitwise ;
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IN: project-euler.046
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! http://projecteuler.net/index.php?section=problems&id=46
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! DESCRIPTION
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! -----------
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! It was proposed by Christian Goldbach that every odd composite number can be
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! written as the sum of a prime and twice a square.
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! 9 = 7 + 2 * 1^2
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! 15 = 7 + 2 * 2^2
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! 21 = 3 + 2 * 3^2
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! 25 = 7 + 2 * 3^2
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! 27 = 19 + 2 * 2^2
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! 33 = 31 + 2 * 1^2
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! It turns out that the conjecture was false.
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! What is the smallest odd composite that cannot be written as the sum of a
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! prime and twice a square?
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! SOLUTION
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! --------
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<PRIVATE
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: perfect-squares ( n -- seq )
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2 /i sqrt >integer [1,b] [ sq ] map ;
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: fits-conjecture? ( n -- ? )
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dup perfect-squares [ 2 * - ] with map [ prime? ] any? ;
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: next-odd-composite ( n -- m )
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dup odd? [ 2 + ] [ 1 + ] if dup prime? [ next-odd-composite ] when ;
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: disprove-conjecture ( n -- m )
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dup fits-conjecture? [ next-odd-composite disprove-conjecture ] when ;
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PRIVATE>
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: euler046 ( -- answer )
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9 disprove-conjecture ;
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! [ euler046 ] 100 ave-time
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! 37 ms ave run time - 3.39 SD (100 trials)
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SOLUTION: euler046
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