Compute blue moons, money bag months, and blue money months

A friend and I got into an argument about money bag months and blue moons. I need a program which determine when future months have both a blue moon(full moon twice in the same month) and months of 31 days where the 1st of the month is a friday. Final output should include the next 5000 years of blue moons and money bag months, as well as money bag months that are also blule moons. Also need average length of time between the months for all three columns. Average between blue moons, between MBM, average between blue money months. For the purpose of this program, the lunar cycle is 29.5306 days. Last full moon was April 17 at 9:44pm. Money Bag month is a 31 day month beginning on a Friday. Leap year, Feb 29, every four years. January, March, May, July, August, October, December have 31 days.