problem 25

problem_25.py

@@ -0,0 +1,24 @@
+
+# The Fibonacci sequence is defined by the recurrence relation:
+#
+# Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
+#
+# The 12th term, F12, is the first term to contain three digits.
+#
+# What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
+
+n_minus_1 = 1
+n_minus_2 = 1
+value = 0
+index = 3
+
+while True:
+
+    value = n_minus_1 + n_minus_2
+    if len(str(value)) == 1000:
+        print(index)
+        break
+
+    n_minus_2 = n_minus_1
+    n_minus_1 = value
+    index += 1

problem_26.py

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+
+# A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
+#
+# 1/2	= 	0.5
+# 1/3	= 	0.(3)
+# 1/4	= 	0.25
+# 1/5	= 	0.2
+# 1/6	= 	0.1(6)
+# 1/7	= 	0.(142857)
+# 1/8	= 	0.125
+# 1/9	= 	0.(1)
+# 1/10	= 	0.1
+
+# Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
+#
+# Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
+
+def longest_permutation(input):
+
+    return input
+
+i = str(1.0/7.0)
+print(i)
+if "142857" in i:
+    print(True)