Determine the smallest value of a positive integer N such that N is a palindrome in both base 3 and base 10. What is the next smallest value of N having this property?
*** N must have more than one digit in any base. So, trivial solutions like (4)base 10 or, (8)base 10 are not permissible.
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
ChDir "C:Program Files (x86)DevStudioVBprojectsflooble"
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
For i = 1 To 1000000
s$ = LTrim(Str$(i))
If isPalin(s$) Then
s$ = base$(i, 3)
If isPalin(s$) Then
Text1.Text = Text1.Text & i & " " & s$ & crlf
End If
End If
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
Function base$(n, b)
v$ = ""
n2 = n
Do
d = n2 Mod b
n2 = n2 b
v$ = Mid("0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ", d + 1, 1) + v$
Loop Until n2 = 0
base$ = v$
End Function
Function isPalin(s$)
good = 1
For i = 1 To Len(s$) / 2
If Mid$(s$, i, 1) <> Mid$(s$, Len(s$) + 1 - i, 1) Then good = 0: Exit For
Next
isPalin = good
End Function
finds
first the completely trivial (the bad):
1 1
2 2
then the semi-trivial (the ugly):
4 11
8 22
and then the expected answer and beyond (the good):
dec base-3
121 11111
151 12121
212 21212
242 22222
484 122221
656 220022
757 1001001
29092 1110220111
48884 2111001112
74647 10210101201
75457 10211111201
76267 10212121201
92929 11201110211
93739 11202120211
848848 1121010101211
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Posted by Charlie
on 2014-09-17 15:42:06 |
computer solution -- the good the bad and the ugly
