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%I #7 Mar 20 2015 23:19:17
%S 11,131,1511,17341,198997,2283583,26205133,300715537,3450844193,
%T 39599967967,454427199648,5214753707584,59841612147821,
%U 686709046151502,7880290940381527,90429834371744720,1037722465625775937
%N a(n) = floor(t^n), where t=3450844193^(1/9) (approximately 11.4754).
%C FEPS(9,1) (first floor exponential prime sequence of length 9).
%C 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.
%C 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_
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see page 69, exercise 1.75.
%e a(4) = floor(t^4) = floor(3450844193^(4/9)) = 17341, which is prime, like each other term in the sequence.
%t Table[ Floor[3450844193^(n/9)], {n, 1, 18}]
%Y Cf. A063636.
%K nonn
%O 1,1
%A David Terr (dterr(AT)wolfram.com), Nov 05 2002
%E Edited and extended by _Robert G. Wilson v_, Nov 07 2002
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