cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A127343 Product of 11 consecutive primes.

This page as a plain text file.
%I A127343 #21 Sep 21 2024 02:28:02
%S A127343 200560490130,3710369067405,50708377254535,436092044389001,
%T A127343 2928046583754721,14107860812636383,64027983688118969,
%U A127343 229747470880897477,810162134158954261,2500935283708076197
%N A127343 Product of 11 consecutive primes.
%C A127343 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 A127343 a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 10}]], {x, 1, 50}]; a
%t A127343 Times@@@Partition[Prime[Range[50]],11,1] (* _Harvey P. Dale_, Oct 21 2011 *)
%o A127343 (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 A127343 (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 A127343 (Magma) [&*[ NthPrime(n+k): k in [0..10] ]: n in [1..50] ]; // _Vincenzo Librandi_, Apr 03 2011
%Y A127343 Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127344.
%K A127343 nonn
%O A127343 1,1
%A A127343 _Artur Jasinski_, Jan 11 2007
%E A127343 Edited by _Klaus Brockhaus_, Jan 21 2007