tasks a-s

Task/Self-referential-sequence/Python/self-referential-sequence.py

@@ -0,0 +1,65 @@
+from itertools import groupby, permutations
+
+def A036058(number):
+    return ''.join( str(len(list(g))) + k
+                    for k,g in groupby(sorted(str(number), reverse=True)) )
+
+def A036058_length(numberstring='0', printit=False):
+    iterations, last_three, queue_index = 1, ([None] * 3), 0
+
+    def A036058(number):
+        # rely on external reverse-sort of digits of number
+        return ''.join( str(len(list(g))) + k
+                        for k,g in groupby(number) )
+
+    while True:
+        if printit:
+            print("  %2i %s" % (iterations, numberstring))
+        numberstring = ''.join(sorted(numberstring, reverse=True))
+        if numberstring in last_three:
+            break
+        assert iterations < 1000000
+        last_three[queue_index], numberstring = numberstring, A036058(numberstring)
+        iterations += 1
+        queue_index +=1
+        queue_index %=3
+    return iterations
+
+def max_A036058_length( start_range=range(11) ):
+    already_done = set()
+    max_len = (-1, [])
+    for n in start_range:
+        sn = str(n)
+        sns = tuple(sorted(sn, reverse=True))
+        if sns not in already_done:
+            already_done.add(sns)
+            size = A036058_length(sns)
+            if size > max_len[0]:
+                max_len = (size, [n])
+            elif size == max_len[0]:
+                max_len[1].append(n)
+    return max_len
+
+lenmax, starts = max_A036058_length( range(1000000) )
+
+# Expand
+allstarts = []
+for n in starts:
+    allstarts += [int(''.join(x))
+                  for x in set(k
+                               for k in permutations(str(n), 4)
+                               if k[0] != '0')]
+allstarts = [x for x in sorted(allstarts) if x < 1000000]
+
+print ( '''\
+The longest length, followed by the number(s) with the longest sequence length
+for starting sequence numbers below 1000000 are:
+  Iterations = %i and sequence-starts = %s.''' % (lenmax, allstarts)   )
+
+print ( '''
+Note that only the first of any sequences with the same digits is printed below.
+(The others will differ only in their first term)''' )
+
+for n in starts:
+    print()
+    A036058_length(str(n), printit=True)