r"""
Python module for OEIS sequence number A005132.

Recaman's sequence: a(0) = 0; for n > 0, a(n) = a(n-1) - n
if that number is positive and not already in the sequence,
otherwise a(n) = a(n-1) + n.

Examples of use.
-----------------------------------------------------------------------
>>> from a005132 import *
>>> print a005132_list(16)
[0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24]
>>> print a005132_offset
0
>>> for x in a005132_list_pairs(6):
...     print x
...
(0, 0)
(1, 1)
(2, 3)
(3, 6)
(4, 2)
(5, 7)
>>> print a005132(3)
6
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a005132_offset', 'a005132_list', 'a005132_list_pairs', 'a005132', 'a005132_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a005132_offset = offset = 0

def a005132_gen(gen):
    """Generator function for the 'Recaman transform'."""
    s, x = set(), 0
    gen.next()
    for t in gen:
        yield x
        x = x - t if x - t > 0 and x - t not in s else x + t
        s.add(x)

def a005132_list(n):
    """Returns a list of the first n >= 0 terms of OEIS sequence A005132."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a005132_gen(count()), n))

def a005132_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), a005132_gen(count())))

def a005132(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(a005132_gen(count()), n-offset, n-offset+1)).pop()