Data update

Task/Pell-numbers/Sidef/pell-numbers.sidef

@@ -0,0 +1,31 @@
+func pell_number(n) {
+    lucasU(2, -1, n)
+}
+
+func pell_lucas_number(n) {
+    lucasV(2, -1, n)
+}
+
+say ("The first 10 Pell numbers: ", 10.of(pell_number).join(", "))
+say ("The first 10 Pell-Lucas numbers: ", 10.of(pell_lucas_number).join(", "))
+
+say "\nFirst 10 rational approximations to √2:"
+{|n| pell_lucas_number(n) / 2 / pell_number(n) }.map(1..10).each {|r|
+    say "#{'%10s' % r.as_frac} =~ #{r.as_float}"
+}
+
+var pell_prime_indices = 10.by {|n| pell_number(n).is_prime }
+say "\nThe first 10 Pell primes: "
+pell_prime_indices.each {|n|
+    say "Pell(#{'%2s' % n}) = #{pell_number(n)}"
+}
+
+say ("\nThe first 10 Newman-Shank-Williams numbers: ",
+    10.of{|n| pell_number(2*n) + pell_number(2*n + 1) }.join(', '))
+
+say "\nThe first 10 Pythagorean triples corresponding to near isosceles right triangles:"
+10.of{|n| pell_number(2*n + 1) }.map {|h|
+    var t = isqrt(h**2 >> 1)
+    assert_eq(t**2 + (t+1)**2, h**2)
+    [t, t+1, h]
+}.each{.say}