r"""
Python module for OEIS sequence number A001333.

Numerators of continued fraction convergents to sqrt(2).

Examples of use.
-----------------------------------------------------------------------
>>> from a001333 import *
>>> print a001333_list(12)
[1, 1, 3, 7, 17, 41, 99, 239, 577, 1393, 3363, 8119]
>>> print a001333_offset
0
>>> for x in a001333_list_pairs(6):
...     print x
...
(0, 1)
(1, 1)
(2, 3)
(3, 7)
(4, 17)
(5, 41)
>>> print a001333(5)
41
-----------------------------------------------------------------------
"""

from itertools import islice, izip

__all__ = ('a001333_offset', 'a001333_list', 'a001333_list_pairs', 'a001333', 'a001333_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a001333_offset = offset = 0

def a001333_gen():
    """Generator function for OEIS sequence A001333."""
    x, y = 1, 1
    while True:
        yield x
        x, y = y, 2*y + x

def a001333_list(n):
    """Returns a list of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a001333_gen(), n))

def a001333_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(izip(xrange(offset, n+offset), a001333_gen()))

def a001333(n):
    """Returns the term with index n >= 0; offset 0."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a001333_gen(), n-offset, n-offset+1)).pop()