NY sequence (2 points)
======================

A new mathematical sequence was published in the New York Times newspaper in 1996. This sequence is defined as follows:

.. math:: a_1 = 2
.. math:: a_{i}  =
      \begin{cases}
      a_{i-1} + INT[\frac{i}{2}], & \mbox{if }  i \mbox{ is even, } i > 1 \\
      a_{i-1} * INT[\frac{i}{2}], & \mbox{if }  i \mbox{ is odd, } i > 1
      \end{cases}

where :math:`INT[x]` means the integer part of x.

These are the first 15 items of this sequence:

2, 3, 3, 5, 10, 13, 39, 43, 172, 177, 885, 891, 5346, 5353, 37471, ...

Write function :py:func:`nytimes` that takes a value ``xmax`` (:py:class:`int`) and returns the first number of the previous sequence that is greater than or equal to ``xmax``. Examples:

.. literalinclude:: test-nytimes.txt
      :language: python
      :lines: 3 - 10

.. note:: You have more tests in file :download:`test-nytimes.txt`