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object HofstadterConway { | |
def pow2(n: Int): Int = (Iterator.fill(n)(2)).product | |
def makeHCSequence(max: Int): Seq[Int] = | |
(0 to max - 1).foldLeft (Vector[Int]()) { (v, idx) => | |
if (idx <= 1) v :+ 1 else v :+ (v(v(idx - 1) - 1) + v(idx - v(idx - 1))) | |
} | |
val max = pow2(20) | |
val maxSeq = makeHCSequence(max) | |
def hcRatio(n: Int, seq: Seq[Int]): Double = seq(n - 1).toDouble / n | |
def maximumHCRatioBetween(a: Int, b: Int): (Int, Double) = | |
Iterator.range(a, b + 1) map (n => (n, hcRatio(n, maxSeq))) maxBy (_._2) | |
lazy val mallowsNumber: Int = | |
((max to 1 by -1) takeWhile (hcRatio(_, maxSeq) < 0.55) last) - 1 | |
def main(args: Array[String]): Unit = { | |
for (n <- 1 to 19) { | |
val (value, ratio) = maximumHCRatioBetween(pow2(n), pow2(n+1)) | |
val message = "Maximum of a(n)/n between 2^%s and 2^%s was %s at %s" | |
println(message.format(n, n+1, ratio, value)) | |
} | |
println("Mallow's number = %s".format(mallowsNumber)) | |
} | |
} |
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