Task: Klarner-Rado sequence







Python: def KlarnerRado(N):
    K = [1]
    for i in range(N):
        j = K[i]
        firstadd, secondadd = 2 * j + 1, 3 * j + 1
        if firstadd < K[-1]:
            for pos in range(len(K)-1, 1, -1):
                if K[pos] < firstadd < K[pos + 1]:
                    K.insert(pos + 1, firstadd)
                    break
        elif firstadd > K[-1]:
            K.append(firstadd)
        if secondadd < K[-1]:
            for pos in range(len(K)-1, 1, -1):
                if K[pos] < secondadd < K[pos + 1]:
                    K.insert(pos + 1, secondadd)
                    break
        elif secondadd > K[-1]:
            K.append(secondadd)

    return K

kr1m = KlarnerRado(100_000)

print('First 100 Klarner-Rado sequence numbers:')
for idx, v in enumerate(kr1m[:100]):
    print(f'{v: 4}', end='\n' if (idx + 1) % 20 == 0 else '')
for n in [1000, 10_000, 100_000]:
    print(f'The {n :,}th Klarner-Rado number is {kr1m[n-1] :,}')


VB: Option Strict On
Option Explicit On

Imports System.IO

Module KlarnerRado

    Private Const bitsWidth As Integer = 31

    Private bitMask() As Integer = _
        New Integer(){ 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 _
                     , 2048, 4096, 8192, 16384, 32768, 65536, 131072 _
                     , 262144, 524288, 1048576, 2097152, 4194304, 8388608 _
                     , 16777216, 33554432, 67108864, 134217728, 268435456 _
                     , 536870912, 1073741824 _
                     }

    Private Const maxElement As Integer = 1100000000


    Private Function BitSet(bit As Integer, v As Integer) As Boolean
        Return (v And bitMask(bit - 1)) <> 0
    End Function

    Private Function SetBit(ByVal bit As Integer, ByVal b As Integer) As Integer
        Return b Or bitMask(bit - 1)
    End Function

    Public Sub Main
        Dim  kr(maxElement \ bitsWidth) As Integer

        For i As Integer = 0 To kr.Count() - 1
            kr(i) = 0
        Next  i

        Dim krCount As Integer =  0    
        Dim n21 As Integer = 3         
        Dim n31 As Integer = 4         
        Dim p10 As Integer = 1000      
        Dim iBit As Integer = 0        
        Dim iOverBw As Integer = 0     
        
        Dim p2Bit As Integer = 1       
        Dim p2OverBw As Integer = 0    
        
        Dim p3Bit As Integer = 1       
        Dim p3OverBw As Integer = 0    

        kr(0) = SetBit(1, kr(0))
        Dim kri As Boolean = True
        Dim lastI As Integer = 0
        For i As Integer = 1 To  maxElement
            iBit += 1
            If iBit > bitsWidth Then
                iBit = 1
                iOverBw += 1
            End If
            If i = n21 Then            
                If BitSet(p2Bit, kr(p2OverBw)) Then
                    kri = True
                End If
                p2Bit += 1
                If p2Bit > bitsWidth Then
                    p2Bit = 1
                    p2OverBw += 1
                End If
                n21 += 2
            End If
            If i = n31 Then            
                If BitSet(p3Bit, kr(p3OverBw)) Then
                    kri = True
                End If
                p3Bit += 1
                If p3Bit > bitsWidth Then
                    p3Bit = 1
                    p3OverBw += 1
                End If
                n31 += 3
            End If
            If kri Then
                lastI = i
                kr(iOverBw) = SetBit(iBit, kr(iOverBw))
                krCount += 1
                If krCount <= 100 Then
                    Console.Out.Write(" " & i.ToString().PadLeft(3))
                    If krCount Mod 20 = 0 Then
                        Console.Out.WriteLine()
                    End If
                ElseIf krCount = p10 Then
                    Console.Out.WriteLine("Element " & p10.ToString().PadLeft(10) & " is " & i.ToString().PadLeft(10))
                    p10 *= 10
                End If
                kri = False
            End If
        Next  i
        Console.Out.WriteLine("Element " & krCount.ToString().PadLeft(10) & " is " & lastI.ToString().PadLeft(10))

    End Sub

End Module