A192324 Sequence of numbers formed as remainder of Mersenne numbers divided by primes.

1, 0, 2, 1, 9, 11, 8, 8, 5, 8, 1, 25, 32, 0, 8, 27, 32, 26, 12, 47, 7, 35, 46, 3, 94, 19, 75, 61, 22, 3, 7, 116, 67, 24, 137, 63, 149, 42, 60, 9, 71, 155, 39, 11, 72, 50, 47, 40, 23, 25, 70, 47, 31, 15, 127, 172, 73, 109, 117, 58, 29, 246, 201, 207, 283, 52, 127, 31, 138, 55, 284, 23

Offset: 1

Author

Pasi Airikka, Jun 28 2011

Keywords

• nonn

Comments

Exponent of Mersenne number formula does not have to be a prime.

Examples

			a(1) = mod(mersenne(1)/prime(1)) = mod(1/2) = 1
a(2) = mod(mersenne(2)/prime(2)) = mod(3/3) = 0
a(3) = mod(mersenne(3)/prime(3)) = mod(7/5) = 2
a(4) = mod(mersenne(4)/prime(4)) = mod(15/7) = 1
a(5) = mod(mersenne(5)/prime(5)) = mod(31/11) = 9
		

Crossrefs

Cf. A000225 (Mersenne), A000040 (prime), A082495.

Programs

MATLAB

% n = number of computed terms of sequence
for i=1:n,
    a(i) = mod(mersenne(i),prime(i)) ;
end

PARI

a(n) = (2^n-1)%prime(n)

PARI

a(n)=lift(Mod(2,prime(n))^n-1) \\ Charles R Greathouse IV, Jun 29 2011

Formula

a(n) = mod (mersenne(n) / prime(n))

where mersenne(n) returns n-th mersenne number and, correspondingly, prime(n) returns n-th prime number.