Pell numbers: Difference between revisions
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(211929657785303, 211929657785304, 299713796309065)
(1235216565974040, 1235216565974041, 1746860020068409)</pre>
=={{header|Wren}}==
{{libheader|Wren-big}}
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<lang ecmascript>import "./big" for BigInt, BigRat
import "./math" for Int
import "./fmt" for Fmt
var p = List.filled(40, 0)
p[0] = 0
p[1] = 1
for (i in 2..39) p[i] = 2 * p[i-1] + p[i-2]
System.print("The first 20 Pell numbers are:")
System.print(p[0..19].join(" "))
var q = List.filled(40, 0)
q[0] = 2
q[1] = 2
for (i in 2..39) q[i] = 2 * q[i-1] + q[i-2]
System.print("\nThe first 20 Pell-Lucas numbers are:")
System.print(q[0..19].join(" "))
System.print("\nThe first 20 rational approximations of √2 (1.4142135623730951) are:")
for (i in 1..20) {
var r = BigRat.new(q[i]/2, p[i])
Fmt.print("$-17s ≈ $-18s", r, r.toDecimal(16, true, true))
}
System.print("\nThe first 15 Pell primes are:")
var p0 = BigInt.zero
var p1 = BigInt.one
var indices = List.filled(15, 0)
var count = 0
var index = 2
var p2
while (count < 15) {
p2 = p1 * BigInt.two + p0
if (Int.isPrime(index) && p2.isProbablePrime(10)) {
System.print(p2)
indices[count] = index
count = count + 1
}
index = index + 1
p0 = p1
p1 = p2
}
System.print("\nIndices of the first 15 Pell primes are:")
System.print(indices.join(" "))
System.print("\nFirst 20 Newman-Shank_Williams numbers:")
var nsw = List.filled(20, 0)
for (n in 0..19) nsw[n] = p[2*n] + p[2*n+1]
Fmt.print("$d", nsw)
System.print("\nFirst 20 near isosceles right triangles:")
p0 = 0
p1 = 1
var sum = 1
var i = 2
while (i < 43) {
p2 = p1 * 2 + p0
if (i % 2 == 1) {
Fmt.print("($d, $d, $d)", sum, sum + 1, p2)
}
sum = sum + p2
p0 = p1
p1 = p2
i = i + 1
}</lang>
{{out}}
<pre style="height:40ex;overflow:scroll;">
The first 20 Pell numbers are:
0 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
The first 20 Pell-Lucas numbers are:
2 2 6 14 34 82 198 478 1154 2786 6726 16238 39202 94642 228486 551614 1331714 3215042 7761798 18738638
The first 20 rational approximations of √2 (1.4142135623730951) are:
1/1 ≈ 1.0000000000000000
3/2 ≈ 1.5000000000000000
7/5 ≈ 1.4000000000000000
17/12 ≈ 1.4166666666666667
41/29 ≈ 1.4137931034482759
99/70 ≈ 1.4142857142857143
239/169 ≈ 1.4142011834319527
577/408 ≈ 1.4142156862745098
1393/985 ≈ 1.4142131979695431
3363/2378 ≈ 1.4142136248948696
8119/5741 ≈ 1.4142135516460547
19601/13860 ≈ 1.4142135642135642
47321/33461 ≈ 1.4142135620573205
114243/80782 ≈ 1.4142135624272734
275807/195025 ≈ 1.4142135623637995
665857/470832 ≈ 1.4142135623746899
1607521/1136689 ≈ 1.4142135623728214
3880899/2744210 ≈ 1.4142135623731420
9369319/6625109 ≈ 1.4142135623730870
22619537/15994428 ≈ 1.4142135623730964
The first 15 Pell primes are:
2
5
29
5741
33461
44560482149
1746860020068409
68480406462161287469
13558774610046711780701
4125636888562548868221559797461449
4760981394323203445293052612223893281
161733217200188571081311986634082331709
2964793555272799671946653940160950323792169332712780937764687561
677413820257085084326543915514677342490435733542987756429585398537901
4556285254333448771505063529048046595645004014152457191808671945330235841
Indices of the first 15 Pell primes are:
2 3 5 11 13 29 41 53 59 89 97 101 167 181 191
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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