58, 76, 97, 104

1 files changed, 35 insertions, 0 deletions

diff --git a/euler104.py b/euler104.py
new file mode 100644
index 0000000..5ec15b4
--- /dev/null
+++ b/euler104.py
@@ -0,0 +1,35 @@
+#!/usr/bin/env python
+
+from math import log10,sqrt
+
+fn_1 = 1
+fn_2 = 1
+n = 3
+
+def pandigital(n):
+    a = [False] * 10
+    while n > 0:
+        t = n % 10
+        if t == 0:
+            return False
+        if a[t]:
+            return False
+        a[t] = True
+        n = n / 10
+    return True
+
+while True:
+    fn = (fn_1 + fn_2) % 1000000000
+    if fn > 100000000 and pandigital(fn):
+        # a[n] = pow((1+sqrt(5))/2, n)/sqrt(5) 
+        #      - pow((1-sqrt(5))/2, n)/sqrt(5)
+        log10_fn = n*log10((1+sqrt(5))/2) - log10(sqrt(5))
+        frac = log10_fn - int(log10_fn)
+        first9 = int(pow(10, frac)*100000000)
+        if pandigital(first9):
+            print(n)
+            break
+
+    fn_2 = fn_1
+    fn_1 = fn
+    n = n + 1