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.

A127344 Product of 12 consecutive primes.

This page as a plain text file.
%I A127344 #18 Sep 20 2024 16:50:00
%S A127344 7420738134810,152125131763605,2180460221945005,20496326086283047,
%T A127344 155186468939000213,832363787945546597,3905707004975257109,
%U A127344 15393080549020130959,57521511525285752531,182568275710689562381,497341164867050876831,1331590860773071702483
%N A127344 Product of 12 consecutive primes.
%C A127344 a(n) = coefficient of x^0 of the polynomial Prod_{j=0,11}(x-prime(n+j)) of degree 12; the roots of this polynomial are prime(n), ..., prime(n+11).
%p A127344 A127344 := proc(n) mul(ithprime(n+k),k=0..11) ; end proc: # _R. J. Mathar_, Apr 05 2011
%t A127344 a = {}; Do[AppendTo[a, Product[Prime[x + n], {n, 0, 11}]], {x, 1, 50}]; a
%t A127344 Times@@@Partition[Prime[Range[50]],12,1] (* _Harvey P. Dale_, Oct 21 2011 *)
%o A127344 (PARI) {m=10;k=12;for(n=0,m-1,print1(a=prod(j=1,k,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 21 2007
%o A127344 (PARI) {m=10;k=12;for(n=1,m,print1(polcoeff(prod(j=0,k-1,(x-prime(n+j))),0),","))} \\ _Klaus Brockhaus_, Jan 21 2007
%o A127344 (Magma) [&*[ NthPrime(n+k): k in [0..11] ]: n in [1..50] ]; // _Vincenzo Librandi_, Apr 03 2011
%Y A127344 Cf. A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127342, A127343.
%K A127344 nonn
%O A127344 1,1
%A A127344 _Artur Jasinski_, Jan 11 2007
%E A127344 Edited by _Klaus Brockhaus_, Jan 21 2007