A127343 - OEIS

%I #21 Sep 21 2024 02:28:02

%S 200560490130,3710369067405,50708377254535,436092044389001,

%T 2928046583754721,14107860812636383,64027983688118969,

%U 229747470880897477,810162134158954261,2500935283708076197

%N Product of 11 consecutive primes.

%C 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).

%t a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 10}]], {x, 1, 50}]; a

%t Times@@@Partition[Prime[Range[50]],11,1] (* _Harvey P. Dale_, Oct 21 2011 *)

%o (PARI) {m=10;k=11;for(n=0,m-1,print1(a=prod(j=1,k,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 21 2007

%o (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

%o (Magma) [&*[ NthPrime(n+k): k in [0..10] ]: n in [1..50] ]; // _Vincenzo Librandi_, Apr 03 2011

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 11 2007

%E Edited by _Klaus Brockhaus_, Jan 21 2007