提问人：Tom Gordon 提问时间：9/20/2023 更新时间：9/20/2023 访问量：14
Collatz 猜想脚本异常、代码错误还是意料之中？
Collatz Conjecture Script Anomaly, Bad Code, or Expected?
问：
我有一个简单的 Collatz 猜想函数，它对一个大（大）整数值执行 3n+1 或 n/2。我将每个 50k 的冰雹数字写入一个文本文件，这样我就可以比较数字，而无需存储每个测试变量的整个 1M 加上冰雹数字。我开始注意到，对于我尝试的几乎每个数字，50k 冰雹数字都是相同的，即使偏离原始数字 $num - [bigint]：:P ow（2， 777） - 1。
我觉得我应该期望这些数字可能会在某个时候达到相同的冰雹数字（显然是 1），但它总是以 50k 的计数击中这一事实对我来说似乎很奇怪。我决定在循环中运行它，并继续减去 2^777-1，看看它退出了多长时间，它确实退出了，但后来它又回来了。当它退出时，它似乎只击中了 1 个数字。我敢肯定，如果我继续下去，它会在 50K 时找到新的东西，但这对我来说似乎很奇怪。我是在代码中遗漏了什么，还是所有这些都是 Collatz 恶作剧的？
Function Get-CC {
[CmdletBinding()]
param(
[Parameter(Mandatory = $false,ValueFromPipeline = $false,ValueFromPipelineByPropertyName = $false,Position = 0)]
[bigint] $IntNum,
[Parameter(Mandatory = $false,ValueFromPipeline = $false,ValueFromPipelineByPropertyName = $false,Position = 1)]
[bigint] $TestNum,
[Parameter(Mandatory = $false,ValueFromPipeline = $false,ValueFromPipelineByPropertyName = $false,Position = 2)]
[bigint] $TestPos=50000
)
$Date = Get-Date -Format "MMddyyyyhhmmss"
if(!(Test-Path -Path "C:\Collatz\$Date")){
New-Item -ItemType Directory -Path "C:\Collatz\$Date" -Force | Out-Null
}
$count = 0
$curFile = "C:\Collatz\$Date\cc$($Date)-$($count).txt"
$IntNum | Out-File -FilePath $curFile
$write = 50000
$add = 50000
While($IntNum -ne 1){
$count++
$even = ($IntNum % 2) -eq 0
if(!$even){
$IntNum = $IntNum * 3 + 1
}else{
$IntNum = $IntNum / 2
}
if($count -eq $TestPos){
if($TestNum -eq $IntNum){
Write-Host "Found test number. Exiting sequence..."
$IntNUm = 1
}else{
$TestNum = $IntNum
}
}
if($count -eq $write){
$lastFile = $curFile
$curFile = "C:\Collatz\$Date\cc$($Date)-$($count).txt"
$IntNum | Out-File -FilePath $curFile
$write = $write + $add
}
}
return @{
Count = $count
Num = $IntNum
TestNum = $TestNum
}
}
$Date = Get-Date -Format "MMddyyyyhhmmss"
$num = [bigint](Get-Content -Path "C:\Collatz\3277.txt")
$TestNum = [bigint](Get-Content -Path "C:\Collatz\09192023030041\cc09192023030041-50000.txt")
for($i=5;$i -lt 100000;$i++){
$newNum = $num - [bigint]::Pow(2, 777) - 1
$num = $newNum
$result = Get-CC -IntNum $num -TestNum $TestNum
$TestNum = $result.TestNum
$result
}
其输出如下。所以 50K 的冰雹要么是 3819......或 9373....即使偏离原始数字 2^777-1。这对我来说似乎很奇怪，但无论如何都很难理解这么大的数字。
PS C:\Windows\system32> E:\Code\Scripts\Scripts\CC from file 4.ps1
Found test number. Exiting sequence...
Name Value
---- -----
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Num 1
Count 3830777
TestNum 937344689765502926333681264218296955864719525763636745876570340903072214591257917645664809522167880706050008910390923047278061123345558...
Num 1
Count 3830777
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Num 1
Count 3830777
TestNum 937344689765502926333681264218296955864719525763636745876570340903072214591257917645664809522167880706050008910390923047278061123345558...
Num 1
Count 3830777
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Num 1
Count 3830777
TestNum 937344689765502926333681264218296955864719525763636745876570340903072214591257917645664809522167880706050008910390923047278061123345558...
Num 1
Count 3830777
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
Found test number. Exiting sequence...
Num 1
Count 50000
TestNum 381928334828457711200301210511765407693780932193463108339714252575226870306253684835311738919785989232887380000099394237942518019339420...
答： 暂无答案
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