Achilles numbers: Difference between revisions

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Here we make use of the fact that powerful numbers are always of the form a²b³, where a and b > 0, to generate such numbers up to a given limit. We also use an improved method for checking whether a number is a perfect power.

Ridiculously fast compared to the previous method: 8 digits now reached in 0.57 seconds, 9 digits in 4.8 seconds and 10 digits in 34 seconds. However, 11 digits takes 300 seconds and I gave up after that.

Ridiculously fast compared to the previous method: 8 digits now reached in 0.57 seconds, 9 digits in 4.2 seconds and 10 digits in 34 seconds. However, 11 digits takes 300 seconds and I gave up after that.

<lang ecmascript>import "./set" for Set, Bag

import "./math" for Int

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}

var getAchilles = Fn.new { |~~digits~~, ~~lower~~|

var getAchilles = Fn.new { |minDigits, maxDigits|

var ~~upper~~ = 10.pow(~~digits~~)

var lower = 10.pow(minDigits)

var upper = 10.pow(maxDigits)

var achilles = Set.new() // avoids duplicates

var count = 0

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}

var achillesSet = getAchilles.call(5, 1) // enough for first 2 parts

var achillesSet = getAchilles.call(1, 5) // enough for first 2 parts

var achilles = achillesSet.toList

achilles.sort()

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System.print("\nNumber of Achilles numbers with:")

for (d in 2..maxDigits) {

var ac = getAchilles.call(d, ~~10.pow(~~d~~-1)~~).count

var ac = getAchilles.call(d-1, d).count

Fmt.print("$2d digits: $d", d, ac)

}</lang>