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

1,3

Comments

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

Links

Table of n, a(n) for n=1..72.

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.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A305178 A295851 A368375 * A063579 A240085 A078623

Adjacent sequences: A192321 A192322 A192323 * A192325 A192326 A192327

Keyword

nonn

Author

Pasi Airikka, Jun 28 2011

Status

approved