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Problem of the Week 1214

A Sine Coincidence? Or Not?

Consider Ceiling[ n/Pi ] and Ceiling[ 1/sin(Pi/n) ], where n ≥ 2 is an integer. The sequences start as follows:

1,2,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,10,...
1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,8,9,9,9,10,...

They differ when n = 3. Are they equal for all larger n?



November 2015