A076255 a(n) = floor(t^n), where t=3450844193^(1/9) (approximately 11.4754).

11, 131, 1511, 17341, 198997, 2283583, 26205133, 300715537, 3450844193, 39599967967, 454427199648, 5214753707584, 59841612147821, 686709046151502, 7880290940381527, 90429834371744720, 1037722465625775937

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.

Links

Table of n, a(n) for n=1..17.

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

Cf. A063636.

Sequence in context: A287295 A227677 A302759 * A076357 A015606 A077417

Adjacent sequences: A076252 A076253 A076254 * A076256 A076257 A076258

Keyword

nonn

Author

David Terr, Nov 05 2002

Extensions

Edited and extended by Robert G. Wilson v, Nov 07 2002

Status

approved