Mertens function: Difference between revisions
Added Swift solution
(Realize in F#) |
(Added Swift solution) |
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92 zeros
59 zero crossings
</pre>
=={{header|Swift}}==
{{trans|C}}
<lang swift>import Foundation
func mertensNumbers(max: Int) -> [Int] {
var mertens = Array(repeating: 1, count: max + 1)
for n in 2...max {
for k in 2...n {
mertens[n] -= mertens[n / k]
}
}
return mertens
}
let max = 1000
let mertens = mertensNumbers(max: max)
let count = 200
let columns = 20
print("First \(count - 1) Mertens numbers:")
for i in 0..<count {
if i % columns > 0 {
print(" ", terminator: "")
}
print(i == 0 ? " " : String(format: "%2d", mertens[i]), terminator: "")
if (i + 1) % columns == 0 {
print()
}
}
var zero = 0, cross = 0, previous = 0
for i in 1...max {
let m = mertens[i]
if m == 0 {
zero += 1
if previous != 0 {
cross += 1
}
}
previous = m
}
print("M(n) is zero \(zero) times for 1 <= n <= \(max).")
print("M(n) crosses zero \(cross) times for 1 <= n <= \(max).")</lang>
{{out}}
<pre>
First 199 Mertens numbers:
1 0 -1 -1 -2 -1 -2 -2 -2 -1 -2 -2 -3 -2 -1 -1 -2 -2 -3
-3 -2 -1 -2 -2 -2 -1 -1 -1 -2 -3 -4 -4 -3 -2 -1 -1 -2 -1 0
0 -1 -2 -3 -3 -3 -2 -3 -3 -3 -3 -2 -2 -3 -3 -2 -2 -1 0 -1
-1 -2 -1 -1 -1 0 -1 -2 -2 -1 -2 -3 -3 -4 -3 -3 -3 -2 -3 -4
-4 -4 -3 -4 -4 -3 -2 -1 -1 -2 -2 -1 -1 0 1 2 2 1 1 1
1 0 -1 -2 -2 -3 -2 -3 -3 -4 -5 -4 -4 -5 -6 -5 -5 -5 -4 -3
-3 -3 -2 -1 -1 -1 -1 -2 -2 -1 -2 -3 -3 -2 -1 -1 -1 -2 -3 -4
-4 -3 -2 -1 -1 0 1 1 1 0 0 -1 -1 -1 -2 -1 -1 -2 -1 0
0 1 1 0 0 -1 0 -1 -1 -1 -2 -2 -2 -3 -4 -4 -4 -3 -2 -3
-3 -4 -5 -4 -4 -3 -4 -3 -3 -3 -4 -5 -5 -6 -5 -6 -6 -7 -7 -8
M(n) is zero 92 times for 1 <= n <= 1000.
M(n) crosses zero 59 times for 1 <= n <= 1000.
</pre>
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