The program below first verifies the logarithmic formula used works for finding Fibonacci numbers, then finds the answer:

The verification of formula validity:

That is, the 2749th Fibonacci number which is approximately 10^574.157538045026 or  1.437268955346967 x 10^574 is the first such number asked for.

A similar program would work for the unasked-for 10-digit pandigital.

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

 Form1.Visible = True

 

 

 Text1.Text = ""

 crlf = Chr$(13) + Chr$(10)

 

 phi = (1 + Sqr(5)) / 2

 lphi = Log(phi) / Log(10)

 l5 = Log(5) / Log(10)

 lFib = lphi - l5 / 2

 For i = 1 To 10

   Text1.Text = Text1.Text & i & "   " & Int(10 ^ lFib + 0.5) & crlf

   lFib = lFib + lphi

 Next

 

 

 

lFib = lphi - l5 / 2: Fibno = 1

Do

  Fibno = Fibno + 1

  lFib = lFib + lphi

  mantissa = lFib - Int(lFib)

  alog = 10 ^ mantissa

  s$ = LTrim(Str(alog))

  ix = InStr(s, ".")

  If ix > 0 Then s = Left(s, ix - 1) + Mid(s, ix + 1)

  good = 1

  For i = 2 To 9

   If Mid(s, i, 1) = "0" Then good = 0: Exit For

   If InStr(s, Mid(s, i, 1)) < i Then good = 0: Exit For

  Next

  If good Then Text1.Text = Text1.Text & Fibno & "   " & lFib & crlf: Exit Do

Loop

 

 

 

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

  

End Sub