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 Representation Initiation (Posted on 2014-05-26)
The base ten integer 839 has the representations 1132 and 11324 respectively in base 9 and base 5. Accordingly, 839 has a base 5 representation that begins with its base 9 representation.

For which other base ten integers between 10 and 2014 inclusively do the base 5 representation of the integer begin with its base 9 representation?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
For n = 10 To 200000
b5\$ = base\$(n, 5)
b9\$ = base\$(n, 9)
If InStr(b5\$, b9\$) = 1 Then
Text1.Text = Text1.Text & Str(n) & "   " & b5\$ & "   " & b9\$ + crlf
DoEvents
End If
Next

End Sub

Function base\$(n, b)
v\$ = ""
n2 = n
Do
d = n2 Mod b
n2 = n2 \ b
v\$ = LTrim(Str(d)) + v\$
Loop Until n2 = 0
base\$ = v\$
End Function

attempts n through 200,000, but finds all the valid numbers under 2000:

`        base   10     5       9  ------------------   839   11324   1132  840   11330   1133  894   12034   1203  895   12040   1204  900   12100   1210 1739   23424   2342 1740   23430   2343 1794   24134   2413 1795   24140   2414 1800   24200   2420`

 Posted by Charlie on 2014-05-26 16:47:35

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