Pell numbers: Difference between revisions
Pell numbers en FreeBASIC
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==={{header|FreeBASIC}}===
{{trans|Phix}}
<lang freebasic>#define isOdd(a) (((a) and 1) <> 0)
Function isPrime(Byval ValorEval As Integer) As Boolean
If ValorEval < 2 Then Return False
If ValorEval Mod 2 = 0 Then Return ValorEval = 2
If ValorEval Mod 3 = 0 Then Return ValorEval = 3
Dim d As Integer = 5
While d * d <= ValorEval
If ValorEval Mod d = 0 Then Return False Else d += 2
If ValorEval Mod d = 0 Then Return False Else d += 4
Wend
Return True
End Function
Dim As Integer n
Dim As Integer p(0 To 40), pl(0 To 40)
p(0)= 0: p(1) = 1
pl(0) = 2: pl(1) = 2
For n = 2 To 40
p(n) = 2 * p(n-1) + p(n-2)
pl(n) = 2 * pl(n-1) + pl(n-2)
Next n
Print "First 20 Pell numbers: "
For n = 0 To 19 : Print p(n); : Next n
Print !"\n\nFirst 20 Pell-Lucas: "
For n = 0 To 19 : Print pl(n); : Next n
Print !"\n\nFirst 20 rational approximations of sqrt(2) (" & Str(Sqr(2)) & "): "
For n = 1 To 20
Dim As Integer j = pl(n)/2, d = p(n)
Print Using " &/& ~= &"; j; d; j/d
Next n
Print !"\nFirst 6 Pell primes: [for the limitations of the FB standard library]"
Dim as Integer pdx = 2
Dim As Byte c = 0
Dim As Ulongint ppdx(1 to 20)
do
If isPrime(p(pdx)) Then
If isPrime(pdx) Then ppdx(c) = pdx : End If
Print p(pdx)
c += 1
End If
pdx += 1
loop until c = 6
Print !"\nIndices of first 6 Pell primes: [for the limitations of the FB standard library]"
For n = 0 To 5 : Print " "; ppdx(n); : Next n
Dim As Ulongint nsw(0 To 20)
For n = 0 To 19
nsw(n) = p(2*n) + p(2*n+1)
Next n
Print !"\n\nFirst 20 Newman-Shank-Williams numbers: "
For n = 0 To 19 : Print " "; nsw(n); : Next n
Print !"\n\nFirst 20 near isosceles right triangles:"
Dim As Integer i0 = 0, i1 = 1, i2, t = 1, i = 2, found = 0
Do While found < 20
i2 = i1*2 + i0
If isOdd(i) Then
Print Using " [&, &, &]"; t; t+1 ; i2
found += 1
End If
t += i2
i0 = i1 : i1 = i2
i += 1
Loop
Sleep</lang>
{{out}}
<pre style="height:40ex;overflow:scroll;">First 20 Pell numbers:
0 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
First 20 Pell-Lucas:
2 2 6 14 34 82 198 478 1154 2786 6726 16238 39202 94642 228486 551614 1331714 3215042 7761798 18738638
First 20 rational approximations of sqrt(2) (1.414213562373095):
1/1 ~= 1
3/2 ~= 1.5
7/5 ~= 1.4
17/12 ~= 1.416666666666667
41/29 ~= 1.413793103448276
99/70 ~= 1.414285714285714
239/169 ~= 1.414201183431953
577/408 ~= 1.41421568627451
1393/985 ~= 1.414213197969543
3363/2378 ~= 1.41421362489487
8119/5741 ~= 1.414213551646055
19601/13860 ~= 1.414213564213564
47321/33461 ~= 1.41421356205732
114243/80782 ~= 1.414213562427273
275807/195025 ~= 1.414213562363799
665857/470832 ~= 1.41421356237469
1607521/1136689 ~= 1.414213562372821
3880899/2744210 ~= 1.414213562373142
9369319/6625109 ~= 1.414213562373087
22619537/15994428 ~= 1.414213562373096
First 6 Pell primes: [for the limitations of the FB standard library]
2
5
29
5741
33461
44560482149
Indices of first 6 Pell primes: [for the limitations of the FB standard library]
2 3 5 11 13 29
First 20 Newman-Shank-Williams numbers:
1 7 41 239 1393 8119 47321 275807 1607521 9369319 54608393 318281039 1855077841 10812186007 63018038201 367296043199 2140758220993 12477253282759 72722761475561 423859315570607
First 20 near isosceles right triangles:
[3, 4, 5]
[20, 21, 29]
[119, 120, 169]
[696, 697, 985]
[4059, 4060, 5741]
[23660, 23661, 33461]
[137903, 137904, 195025]
[803760, 803761, 1136689]
[4684659, 4684660, 6625109]
[27304196, 27304197, 38613965]
[159140519, 159140520, 225058681]
[927538920, 927538921, 1311738121]
[5406093003, 5406093004, 7645370045]
[31509019100, 31509019101, 44560482149]
[183648021599, 183648021600, 259717522849]
[1070379110496, 1070379110497, 1513744654945]
[6238626641379, 6238626641380, 8822750406821]
[36361380737780, 36361380737781, 51422757785981]
[211929657785303, 211929657785304, 299713796309065]
[1235216565974040, 1235216565974041, 1746860020068409]</pre>
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