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

Author

David Terr, Nov 05 2002

Keywords

• nonn

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

Examples

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

References

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

Crossrefs

Cf. A063636.

Programs

Mathematica

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

Extensions

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