Option Explicit

Dim cT      As New CTiming

Private Sub Form_Load()
Dim i   As Long
Dim n   As Long

    Open "resultados.txt" For Binary As #1
    
    cT.Reset
    For i = 0 To 10000
        Call IsOblongo01(i, n)
    Next i

    Put #1, , "Karcrack -> " & cT.sElapsed & vbCrLf

    cT.Reset
    For i = 0 To 10000
        Call EsOblongo(i, n)
    Next i
    Put #1, , "Tokes -> " & cT.sElapsed & vbCrLf
    
    cT.Reset
    For i = 0 To 10000
        Call IsOblongoLeo2(i, n)
    Next i
    Put #1, , "LeandroA -> " & cT.sElapsed
    
    Close #1
    End
End Sub
 
' Karcrack
Private Function IsOblongo01(ByVal lNumb As Long, ByRef n As Long) As Boolean
    If (lNumb = 0) Then n = 0: IsOblongo01 = True: Exit Function
 
    If (lNumb And 1) = 0 Then
        For n = 1 To Sqr(lNumb + 1)
            If lNumb = n * (n + 1) Then
                IsOblongo01 = True
                Exit For
            End If
        Next n
    End If
End Function
 
'Tokes
Private Function EsOblongo(ByVal num As Long, ByRef n As Long) As Boolean
Dim max As Long, i As Long
    If (num And 1) Then Exit Function
 
    max = Sqr(num)
    For i = 0 To max
        If num = i * i + i Then 'i * (i + 1) Then
            EsOblongo = True
            n = i
            Exit Function
        End If
    Next
End Function
 
' LeandroA
Private Function IsOblongoLeo2(ByVal lNumb As Long, ByRef n As Long) As Boolean
    Dim lmax As Long, i As Long
 
    If (lNumb And 1) Then Exit Function
    If lNumb = 0 Then n = 0: IsOblongoLeo2 = True: Exit Function
 
    lmax = Sqr(lNumb)
 
    For i = lmax - 1 To lmax
        If lNumb = i * (i + 1) Then
            IsOblongoLeo2 = True
            n = i
            Exit Function
        End If
    Next
End Function

Karcrack -> 5,514 msec
Tokes -> 5,603 msec
LeandroA -> 1,576 msec

Pronic numbers can also be expressed as n² + n. The n-th pronic number is the sum of the first n even integers, as well as the difference between (2n − 1)² and the n-th centered hexagonal number.

All pronic numbers are even, therefore 2 is the only prime pronic number. It is also the only pronic number in the Fibonacci sequence.

The number of off-diagonal entries in a square matrix is always a pronic number.

The value of the Möbius function μ(x) for any pronic number x = n (n + 1), in addition to being computable in the usual way, can also be calculated as

    μ(x) = μ(n) μ(n + 1).

The fact that consecutive integers are coprime and that a pronic number is the product of two consecutive integers leads to a number of properties. Each distinct prime factor of a pronic number is present in only one of its factors. Thus a pronic number is squarefree if and only if n and n + 1 are. The number of distinct prime factors of a pronic number is the sum of the number of distinct prime factors of n and n + 1.