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
Examples
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.
Programs
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Mathematica
Table[Mod[Product[Prime[k + 1], {k, n}], Sum[Prime[k + 1], {k, n}]], {n, 60}] (* Michael De Vlieger, Oct 02 2015 *) -
PARI
a(n) = prod(k=1, n, prime(k+1)) % sum(k=1, n, prime(k+1)); vector(60, n, a(n))
Comments