Advance Happy New Year, 2016!

Mathematica, 45 37 27 24 bytes

#+5[6,6,11][[#~Mod~4]]&

Improvements thanks to @MartinBüttner (10 bytes), and @ChipHurst (a further 3 bytes).

CJam, 21 12 11 bytes

{_9587Cb=+}

@martin found a very simple method!

Try it here.

EDIT: Thanks, Dennis!

gs2, 12 bytes

V@¶4☻s%☺♀i50

Translation of my CJam answer. Encoded in CP437 as usual. Try it online!