Integer#zeisel?: Add

lib/numb.rb

@@ -17,7 +17,7 @@
           smarandache_wellin smith smooth sophie_germain_prime sphenic square
           square_free sublime sum_of_squares superabundant superperfect totient
           triangular trimorphic undulating unitary_perfect unitary_divisor 
-          untouchable vampire weird
+          untouchable vampire weird zeisel
 }
 
 class Integer

lib/numb/zeisel.rb

@@ -0,0 +1,13 @@
+class Integer
+  def zeisel?
+    return false unless square_free? and (p=prime_factors.sort.uniq).size >= 3
+    p.unshift(1)
+    (1..p.max).any? do |a|
+      b = p[1] - (a*p[0])
+      p.each_with_index.all? do |n, i|
+        next true if i.zero?
+        n == (a*p[i-1]) + b
+      end
+    end
+  end
+end 

spec/zeisel_spec.rb

@@ -0,0 +1,20 @@
+describe Integer, "#zeisel?" do
+  # A051015
+  ZEISEL = [105,1419,1729,1885,4505,5719,15387,24211,25085,
+            27559,31929,54205,59081,114985,207177,208681,
+            233569,287979,294409,336611,353977,448585,507579,
+            721907,982513,1012121,1073305,1242709,1485609,
+            2089257,2263811,2953711,3077705,3506371,3655861,
+            3973085,4648261,5069629,6173179,6253085,6985249,
+            7355239,7355671,7558219,8011459,8413179,8444431,
+            8712985,9271805,9773731,15411785,18175361,
+            18578113,19827641,20771801,23691481,26000605,
+            26758057]
+
+  # 721907 appears to be in this sequence by error...
+  (ZEISEL - [721907]).each do |n|
+    it "should return true for Zeisel number #{n}" do
+      n.should be_zeisel
+    end
+  end
+end