r"""
Python module for OEIS sequence number A004001.

Hofstadter-Conway $10000 sequence:
a(1) = a(2) = 1; for n > 2, a(n) = a(a(n-1)) + a(n-a(n-1)).

Examples of use.
-----------------------------------------------------------------------
>>> from a004001 import *
>>> print a004001_list(18)
[1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 8, 8, 8, 9, 10]
>>> print a004001_offset
1
>>> for x in a004001_list_pairs(6):
...     print x
...
(1, 1)
(2, 1)
(3, 2)
(4, 2)
(5, 3)
(6, 4)
>>> print a004001(100)
57
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a004001_offset', 'a004001_list', 'a004001_list_pairs', 'a004001', 'a004001_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a004001_offset = offset = 1

def a004001_gen():
    """Generator function for OEIS sequence A004001."""
    a = {1:1, 2:1}
    yield a[1]
    yield a[2]
    for n in count(3):
        a[n] = a[a[n-1]] + a[n-a[n-1]]
        yield a[n]

def a004001_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(a004001_gen(), n))

def a004001_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(a004001_offset, n+a004001_offset), a004001_gen()))

def a004001(n):
    """Returns the term with index n >= 1; offset 1."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a004001_gen(), n-a004001_offset, n-a004001_offset+1)).pop()