A262807 a(n) = (Product_{k=1..n} prime(k+1)) mod (Sum_{k=1..n} prime(k+1)) where prime(k) is the k-th prime number.

0, 7, 0, 11, 0, 7, 45, 91, 24, 55, 0, 113, 93, 175, 308, 153, 414, 395, 273, 355, 609, 779, 558, 23, 0, 843, 962, 185, 0, 547, 1634, 21, 170, 1149, 1455, 2483, 1830, 2275, 2865, 1989, 0, 1515, 1211, 2013, 1105, 403, 2733, 819, 0, 4011, 0, 1457, 4278, 1155, 391, 1717, 2596, 2163, 0, 5985

Offset

1,2

Comments

Remainder when product of first n odd primes is divided by sum of first n odd primes.

Obviously a(2n) cannot be 0. Does 0 appear in the sequence infinitely often?

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = A070826(n+1) mod A071148(n).

Example

a(1) = prime(2) mod prime(2) = 3 mod 3 = 0.
a(2) = (prime(2) * prime(3)) mod (prime(2) + prime(3)) = 15 mod 8 = 7.
a(3) = (prime(2) * prime(3) * prime(4)) mod (prime(2) + prime(3) + prime(4)) = 105 mod 15 = 0.
a(4) = (prime(2) * prime(3) * prime(4) * prime(5)) mod (prime(2) + prime(3) + prime(4) + prime(5)) = 1155 mod 26 = 11.

Mathematica

Table[Mod[Product[Prime[k + 1], {k, n}], Sum[Prime[k + 1], {k, n}]], {n, 60}] (* Michael De Vlieger, Oct 02 2015 *)

Prog

(PARI) a(n) = prod(k=1, n, prime(k+1)) % sum(k=1, n, prime(k+1));
vector(60, n, a(n))

Crossrefs

Cf. A065091, A070826, A071089, A071148, A259643.

Sequence in context: A096408 A005481 A122699 * A169603 A022920 A331423

Adjacent sequences: A262804 A262805 A262806 * A262808 A262809 A262810

Keyword

nonn,easy

Author

Altug Alkan, Oct 02 2015

Status

approved