--- In

primenumbers@yahoogroups.com,

"David Broadhurst" <d.broadhurst@...> wrote:

> http://www.research.att.com/~njas/sequences/A097074

> shows that the sequence is

> a(n) = 2*(2^(n+1) + (-1)^n)/3 - 1

a(2*k-2) = (4^k - 1)/3 is clearly composite for k > 2.

a(2*k-1) = (2*4^k - 5)/3 is a unit for k = 1, a prime for

k = 3, 6, 9, 15, 25, 27, 42, 55, 159, 186, 252, 405, 450, 471, 558,

a probable prime for

k = 1099, 1215, 2529, 4711, 6300, 10147, 11377,

and composite for all other positive integers k < 15600.

The sequence of primes of the form N = (2*4^k - 5)/3

shares a feature with the Wagstaff sequence

http://primes.utm.edu/top20/page.php?id=67
since in the present case one or both of

N - 1 = 8*(4^(k-1) - 1)/3

N + 1 = 2*(4^k - 1)/3

may have many prime factors recorded by the

Cunningham project and its extensions.

Thus I easily proved primality for k = 6300:

Calling N+1 BLS with factored part 52.49%

and helper 0.17% (157.63% proof)

(2*4^6300-5)/3 is prime! (22.9328s+0.0190s)

at 3793 decimal digits.

Can someone prove primality of a larger member of A97074 ?

David