1,1

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

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see page 69, exercise 1.75.

a(4)=Floor[t^4]=Floor[3450844193^(4/9)]=17341, which is prime, like each other term in the sequence.

Table[ Floor[3450844193^(n/9)], {n, 1, 18}]

Cf. A063636.

Sequence in context: A140004 A100758 A083763 this_sequence A076357 A015606 A077417

Adjacent sequences: A076252 A076253 A076254 this_sequence A076256 A076257 A076258

nonn

David Terr (dterr(AT)wolfram.com), Nov 05 2002

Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 07 2002