Power Floor Prime Sequence

A power floor prime sequence is a sequence of prime numbers , where  is the floor function and  is real number. It is unknown if, though extremely unlikely that, infinite sequences of this type exist. An example having eight consecutive primes is , which gives 2, 5, 13, 31, 73, 173, 409, and 967 and has the smallest possible numerator and denominators for an 8-term sequence (D. Terr, pers. comm., Sep. 1, 2004). D. Terr (pers. comm., Jan. 21, 2003) has found a sequence of length 100.

REFERENCES:

Crandall, R. and Pomerance, C. Prime Numbers: A Computational Perspective, 2nd ed. New York: Springer-Verlag, 2005.