A317977 a(n) = A003010(n-2) mod (2^n - 1).

1, 0, 14, 0, 23, 0, 149, 205, 95, 1736, 779, 0, 4193, 20400, 25439, 0, 221468, 0, 1036394, 840107, 1751891, 6107895, 5639594, 8772568, 66322529, 60611448, 99083624, 458738443, 989927528, 0, 3038229779, 5238898821, 393215, 11960838285, 27264928469, 117093979072, 274827575393, 276971366821

Offset: 2

Author

Thomas Ordowski, Aug 12 2018

Keywords

• nonn

Comments

For n > 2, the Mersenne number 2^n - 1 is a prime if and only if a(n) = 0. See comments in A003010.

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..3322

Crossrefs

Cf. A000043, A000225, A000668, A003010, A095847.

Programs

PARI

a(n) = {my(pow = 2^n-1, res = Mod(4, pow)); for(i = 1, n-2, res = res^2 - 2); lift(res)}
first(n) = vector(n, i, a(i+1)) \\ David A. Corneth, Aug 12 2018

Python

def A317977(n):
    m = 2**n-1
    c = 4 % m
    for _ in range(n-2):
        c = (c**2-2) % m
    return c # Chai Wah Wu, Oct 08 2018

Formula

a(prime(n)) = A095847(n).

Extensions

More terms from Michel Marcus and David A. Corneth, Aug 12 2018