r"""
Python module for OEIS sequence number A046901.

a(n) = a(n-1) - n if a(n-1) > n, else a(n) = a(n-1) + n.

Examples of use.
-----------------------------------------------------------------------
>>> from a046901 import *
>>> print a046901_list(18)
[1, 3, 6, 2, 7, 1, 8, 16, 7, 17, 6, 18, 5, 19, 4, 20, 3, 21]
>>> print a046901_offset
1
>>> for x in a046901_list_pairs(6):
...     print x
...
(1, 1)
(2, 3)
(3, 6)
(4, 2)
(5, 7)
(6, 1)
>>> print a046901(4)
2
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a046901_offset', 'a046901_list', 'a046901_list_pairs', 'a046901', 'a046901_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a046901_offset = offset = 1

def a046901_gen():
    """Generator function for OEIS sequence A046901."""
    x = 0
    for n in count(1):
        x = x - n if x - n > 0 else x + n
        yield x

def a046901_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(a046901_gen(), n))

def a046901_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), a046901_gen()))

def a046901(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(a046901_gen(), n-offset, n-offset+1)).pop()