16

This number is a composite.

16 is the largest number n which has the property of adding n to itself and subtracting 1, then continuing the process by adding half of n and subtraction 1 each iteration to produce primes at each step: 16+16-1 = 31, 16+8-1 = 23, 16+4-1 = 19, 16+2-1 = 17. [Sariyar]