Power Floor Prime Sequence

A power floor prime sequence is a sequence of prime numbers {|_theta^n_|}_n, where |_x_| is the floor function and theta>1 is real number. It is unknown if, though extremely unlikely that, infinite sequences of this type exist. An example having eight consecutive primes is theta=111/47, 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.

See also

Mills' Constant, Mills' Theorem, Power Floors, Prime Number

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

Referenced on Wolfram|Alpha

Power Floor Prime Sequence

Cite this as:

Weisstein, Eric W. "Power Floor Prime Sequence." From MathWorld--A Wolfram Web Resource.

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