Find the smallest Fibonacci number with a prime subscript but not prime itself.
The smallest Fibonacci number with a prime subscript but itself composite:
The first 30 Fibo numbers and their smallest prime divisors:
1 1 1
2 1 1
3 2 2
4 3 3
5 5 5
6 8 2
7 13 13
8 21 3
9 34 2
10 55 5
11 89 89
12 144 2
13 233 233
14 377 13
15 610 2
16 987 3
17 1597 1597
18 2584 2
19 4181 37
19 4181
20 6765 3
21 10946 2
22 17711 89
23 28657 28657
24 46368 2
25 75025 5
26 121393 233
27 196418 2
28 317811 3
29 514229 514229
30 832040 2
F(19) = 4181 = 37 * 113 is the solution to this similar puzzle.
DefDbl A-Z
Dim wd(10) As String, w As String, sz, crlf$
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
fibn = 0: fibnp1 = 1
For n = 1 To 30
h = fibn + fibnp1
fibn = fibnp1: fibnp1 = h
Text1.Text = Text1.Text & mform(n, "###") & mform(fibn, "########") & mform(prmdiv(fibn), "#######") & crlf
If prmdiv(n) = n And prmdiv(fibn) < fibn Then
Text1.Text = Text1.Text & mform(n, "###") & mform(fibn, "######") & crlf
End If
Next
End Sub
Function prmdiv(num)
Dim n, dv, q
If num = 1 Then prmdiv = 1: Exit Function
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
Loop
If n > 1 Then prmdiv = n
Exit Function
DivideIt:
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
prmdiv = dv: Exit Function
Else
Exit Do
End If
Loop
Return
End Function
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Posted by Charlie
on 2014-08-06 11:22:46 |
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