A112927 a(n) is the least prime such that the multiplicative order of 2 mod a(n) equals n, or a(n)=1 if no such prime exists.

1, 3, 7, 5, 31, 1, 127, 17, 73, 11, 23, 13, 8191, 43, 151, 257, 131071, 19, 524287, 41, 337, 683, 47, 241, 601, 2731, 262657, 29, 233, 331, 2147483647, 65537, 599479, 43691, 71, 37, 223, 174763, 79, 61681