What is the first term in the Fibonacci sequence to contain 1000 digits?
Notes:
Generator written and saved in projecteuler. Super easy deal.
For large fib vals,
F(n) = round(phi**n / sqrt(5))
phi**n / sqrt(5) > 10**999
n * log(phi) - .5 * log(5) > 999 * log(10)
"""
from math import log
from projecteuler import fibonacci
if __name__ == '__main__':
# Generator way
for (i, f) in enumerate(fibonacci()):
if f / 10**999:
break
print 'the {}-th term is\n\n{}\n'.format(i + 1, f)
# Math way
phi = 1.6180
n = (999. * log(10.) + .5 * log(5)) / log(phi)
print 'By Great Maths we have i = {}'.format(n)
from projecteuler import fibonacci L = 30 # Limit is expressed as 2^L print "Project Euler 301 Solution =", fibonacci(L + 2)
Notes:
Generator written and saved in projecteuler. Super easy deal.
For large fib vals,
F(n) = round(phi**n / sqrt(5))
phi**n / sqrt(5) > 10**999
n * log(phi) - .5 * log(5) > 999 * log(10)
"""
from math import log
from projecteuler import fibonacci
if __name__ == '__main__':
# Generator way
for (i, f) in enumerate(fibonacci()):
if f / 10**999:
break
print 'the {}-th term is\n\n{}\n'.format(i + 1, f)
# Math way
phi = 1.6180
n = (999. * log(10.) + .5 * log(5)) / log(phi)
print 'By Great Maths we have i = {}'.format(n)
from projecteuler import fibonacci L = 30 # Limit is expressed as 2^L print "Project Euler 301 Solution =", fibonacci(L+2)