A127343 Product of 11 consecutive primes.

200560490130, 3710369067405, 50708377254535, 436092044389001, 2928046583754721, 14107860812636383, 64027983688118969, 229747470880897477, 810162134158954261, 2500935283708076197

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

a(n) is the absolute value of the coefficient of x^0 of the polynomial Product_{j=0..10} (x-prime(n+j)) of degree 11; the roots of this polynomial are prime(n), ..., prime(n+10).

Crossrefs

Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127344.

Programs

Magma

[&*[ NthPrime(n+k): k in [0..10] ]: n in [1..50] ]; // Vincenzo Librandi, Apr 03 2011

Mathematica

a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 10}]], {x, 1, 50}]; a
Times@@@Partition[Prime[Range[50]],11,1] (* Harvey P. Dale, Oct 21 2011 *)

PARI

{m=10;k=11;for(n=0,m-1,print1(a=prod(j=1,k,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 21 2007

PARI

{m=10;k=11;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),0)),","))} \\ Klaus Brockhaus, Jan 21 2007

Extensions

Edited by Klaus Brockhaus, Jan 21 2007