List all the positive integers which are equal to the sum of the digits of their respective cubes.
How many of them are prime?
n cube
1 1
8 512
17 4913 prime
18 5832
26 17576
27 19683
Only 17 is prime.
The cube of a 3-digit number will have at most 9 digits, totaling at most 9*9 = 81, and similarly for larger numbers. Thus the above is complete.
For n = 1 To 100
DoEvents
n3$ = LTrim(Str(n * n * n))
t = 0
For i = 1 To Len(n3)
t = t + Val(Mid(n3, i, 1))
Next
If t = n Then
Text1.Text = Text1.Text & n & " " & n3 & " "
If prmdiv(n) = n And n > 1 Then Text1.Text = Text1.Text & "prime"
Text1.Text = Text1.Text & crlf
End If
Next
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
|
|
Posted by Charlie
on 2018-12-11 11:08:27 |
computer solution
