DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 For n1 = 100 To 999

   n2 = 100 * (n1 Mod 10) + 10 * ((n1 \ 10) Mod 10) + n1 \ 100

   n = 1000 * n1 + n2

   n1s$ = LTrim(Str(n1))

   n2s$ = LTrim(Str(n2))

   If fromBase(n1s, 9) = fromBase(n2s, 7) Then

     Text1.Text = Text1.Text & n & " " & Str(fromBase(n1s, 9)) & crlf

   End If

   xx = xx

 Next

 

 Text1.Text = Text1.Text & crlf & " done"

  

End Sub

Function fromBase(n$, b)

  v = 0

  For i = 1 To Len(n$)

    c$ = LCase$(Mid(n$, i, 1))

    If c$ > " " Then

      v = v * b + InStr("0123456789abcdefghijklmnopqrstuvwxyz", c$) - 1

    End If

  Next

  fromBase = v

End Function

provides two pseudo-answers and the real answer:

182281  155

305503  248

487784  403

The pseudoanswers first:

When 182 is treated as if it were a base-9 number, its value is 155. Then, while 281 can't really be a base-7 number, we could still treat it as if it could: 2*7^2 + 8*7 + 1 = 155. A similar thing happens when 784 is converted from base 7, as if 8 were a valid base-7 digit; it comes out to the same 403 in decimal that 487 comes out when treated as a base-9 number.

The true sought answer is the 305 in base 9 is the same as 503 in base 7, as each is 248 in decimal notation.

But the puzzle asks for N's prime factorization.

so N happens to be a semiprime.