Pell numbers: Difference between revisions
Added Go
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[1235216565974040, 1235216565974041, 1746860020068409]</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<lang go>package main
import (
"fmt"
"math/big"
"rcu"
)
func main() {
p := make([]int64, 40)
p[1] = 1
for i := 2; i < 40; i++ {
p[i] = 2*p[i-1] + p[i-2]
}
fmt.Println("The first 20 Pell numbers are:")
fmt.Println(p[0:20])
q := make([]int64, 40)
q[0] = 2
q[1] = 2
for i := 2; i < 40; i++ {
q[i] = 2*q[i-1] + q[i-2]
}
fmt.Println("\nThe first 20 Pell-Lucas numbers are:")
fmt.Println(q[0:20])
fmt.Println("\nThe first 20 rational approximations of √2 (1.4142135623730951) are:")
for i := 1; i <= 20; i++ {
r := big.NewRat(q[i]/2, p[i])
fmt.Printf("%-17s ≈ %-18s\n", r, r.FloatString(16))
}
fmt.Println("\nThe first 15 Pell primes are:")
p0 := big.NewInt(0)
p1 := big.NewInt(1)
p2 := big.NewInt(0)
two := big.NewInt(2)
indices := make([]int, 15)
for index, count := 2, 0; count < 15; index++ {
p2.Mul(p1, two)
p2.Add(p2, p0)
if rcu.IsPrime(index) && p2.ProbablyPrime(15) {
fmt.Println(p2)
indices[count] = index
count++
}
p0.Set(p1)
p1.Set(p2)
}
fmt.Println("\nIndices of the first 15 Pell primes are:")
fmt.Println(indices)
fmt.Println("\nFirst 20 Newman-Shank_Williams numbers:")
nsw := make([]int64, 20)
for n := 0; n < 20; n++ {
nsw[n] = p[2*n] + p[2*n+1]
}
fmt.Println(nsw)
fmt.Println("\nFirst 20 near isosceles right triangles:")
u0 := 0
u1 := 1
sum := 1
for i := 2; i < 43; i++ {
u2 := u1*2 + u0
if i%2 == 1 {
fmt.Printf("(%d, %d, %d)\n", sum, sum+1, u2)
}
sum += u2
u0 = u1
u1 = u2
}
}</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>
=={{header|J}}==
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