Data commit

Task/Pell-numbers/Go/pell-numbers.go

@@ -0,0 +1,74 @@
+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
+    }
+}