These are the numbers below 3000 that can be so formed:
(I interpreted this as that each one must be expressible using each n from 1 to 10, not just one of those.)
1009
1129
1201
1801
2521
2689
The specifics:
prime a n b
1009 15 1 28
1009 28 1 15
1009 19 2 18
1009 31 3 4
1009 15 4 14
1009 17 5 12
1009 25 6 8
1009 1 7 12
1009 19 8 9
1009 28 9 5
1009 3 10 10
1129 20 1 27
1129 27 1 20
1129 29 2 12
1129 19 3 16
1129 27 4 10
1129 2 5 15
1129 23 6 10
1129 11 7 12
1129 29 8 6
1129 20 9 9
1129 33 10 2
1201 24 1 25
1201 25 1 24
1201 7 2 24
1201 1 3 20
1201 25 4 12
1201 34 5 3
1201 5 6 14
1201 33 7 4
1201 7 8 12
1201 25 9 8
1201 29 10 6
1801 24 1 35
1801 35 1 24
1801 1 2 30
1801 37 3 12
1801 35 4 12
1801 26 5 15
1801 25 6 14
1801 3 7 16
1801 1 8 15
1801 35 9 8
1801 19 10 12
2521 35 1 36
2521 36 1 35
2521 37 2 24
2521 13 3 28
2521 35 4 18
2521 46 5 9
2521 11 6 20
2521 27 7 16
2521 37 8 12
2521 35 9 12
2521 39 10 10
2689 33 1 40
2689 40 1 33
2689 49 2 12
2689 31 3 24
2689 33 4 20
2689 22 5 21
2689 17 6 20
2689 41 7 12
2689 49 8 6
2689 40 9 11
2689 27 10 14
DefDbl A-Z
Dim crlf$, soln(100)
Function mform$(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
Do
p = nxtprm(p)
good1 = 1
For n = 1 To 10
good = 0
For a = 0 To Sqr(p)
a2 = a * a
diff = p - a2
b = Int(Sqr(diff / n) + 0.5)
If b * b * n = diff Then good = 1: Exit For
Next a
If good = 0 Then good1 = 0
Next n
If good1 Then
Text1.Text = Text1.Text & p & crlf
goodct = goodct + 1
soln(goodct) = p
End If
DoEvents
Loop Until p > 3000
p = 0
Do
p = nxtprm(p)
good1 = 1
For n = 1 To 10
good = 0
For a = 0 To Sqr(p)
a2 = a * a
diff = p - a2
b = Int(Sqr(diff / n) + 0.5)
If b * b * n = diff Then
oneOfThem = 0
For i = 1 To goodct
If soln(i) = p Then
Text1.Text = Text1.Text & p & mform(a, "###0") & mform(n, "###0") & mform(b, "###0") & crlf
End If
Next
End If
Next a
If good = 0 Then good1 = 0
Next n
If good1 Then
Text1.Text = Text1.Text & p & crlf
goodct = goodct + 1
soln(goodct) = p
End If
DoEvents
Loop Until p > 3000
Text1.Text = Text1.Text & " done"
End Sub
Function prm(i)
Dim p As Long
Open "17-bit primes.bin" For Random As #111 Len = 4
Get #111, i, p
prm = p
Close 111
End Function
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
Function nxtprm(x)
Dim n
n = x + 1
While prmdiv(n) < n Or n < 2
n = n + 1
Wend
nxtprm = n
End Function
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Posted by Charlie
on 2018-08-18 14:36:33 |
computer solution
