r"""
Python module for OEIS sequence number A078759.

Height of n-th term in A064389 (variation (4) of Recaman's sequence).

Examples of use.
-----------------------------------------------------------------------
>>> from a078759 import *
>>> print a078759_list(18)
[1, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6]
>>> print a078759_offset
1
>>> for x in a078759_list_pairs(6):
...     print x
...
(1, 1)
(2, 2)
(3, 3)
(4, 2)
(5, 3)
(6, 4)
>>> print a078759(4)
2
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a078759_offset', 'a078759_list', 'a078759_list_pairs', 'a078759', 'a078759_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a078759_offset = offset = 1

def a078759_gen():
    """Generator function for OEIS sequence A078759."""
    s, x, k = set(), 0, 0
    for n in count(1):
        y = x
        m = -n
        j = -1
        x = y + m
        while not (x > 0 and x not in s):
            m = -m if m < 0 else -(m + 1)
            j = -j
            x = y + m
        s.add(x)
        k += j
        yield k

def a078759_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(a078759_gen(), n))

def a078759_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), a078759_gen()))

def a078759(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(a078759_gen(), n-offset, n-offset+1)).pop()