I'm still looking for good rules for phi, [...]

http://cp4space.wordpress.com/2012/09/12/lunisolar-calendars/ I briefly mentioned the use of the Rabbit sequence to optimally approximate a leap year of length 364 + phi. Just choose your favourite rule for generating it: http://en.wikipedia.org/wiki/Rabbit_sequence I seem to recall that there was a Google Turing machine thingy that generated the Rabbit sequence. Sincerely, Adam P. Goucher