OFFSET
1,1
COMMENTS
FEPS(9,1) (first floor exponential prime sequence of length 9).
A floor exponential prime sequence (FEPS) is a sequence of the form {a(n) = floor[t^n]:1<=n<=length} in which t is a real number greater than or equal to 2 and each term in the sequence is prime. FEPS(len,k) is the k-th maximal optimal floor exponential prime sequence of length len, ordered by exponent t = a(len)^(1/len). As far as I know, the only previously known FEPS was FEPS(8,1) = {2, 5, 13, 31, 73, 173, 409, 967} (first 8 terms of A063636). During the past few days I've discovered 20 others with length up to 92, including 16 of length up to 27 which I know to be the first such sequence of given length.
I found that past the first nine members, the only other powers of t which produce a prime are 15, 79 & 101 and no others <= 2500. - Robert G. Wilson v
REFERENCES
R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see page 69, exercise 1.75.
EXAMPLE
a(4) = floor(t^4) = floor(3450844193^(4/9)) = 17341, which is prime, like each other term in the sequence.
MATHEMATICA
Table[ Floor[3450844193^(n/9)], {n, 1, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
David Terr, Nov 05 2002
EXTENSIONS
Edited and extended by Robert G. Wilson v, Nov 07 2002
STATUS
approved