cp's OEIS Frontend

A127340 Primes that are the sum of 11 consecutive primes.

%I A127340 #21 Sep 21 2024 02:28:46
%S A127340 233,271,311,353,443,491,631,677,883,1367,1423,1483,1543,1607,1787,
%T A127340 1901,1951,2011,2141,2203,2383,3253,3469,3541,3617,3691,3967,4159,
%U A127340 4229,4297,4943,5009,5483,5657,5741,5903,5981,6553,6871,6991,7057,7121,7187,7873
%N A127340 Primes that are the sum of 11 consecutive primes.
%C A127340 Primes in A127338.
%C A127340 A prime number n is in the sequence if for some k it is the absolute value of coefficient of x^10 of the polynomial Prod_{j=0,10}(x-prime(k+j)); the roots of this polynomial are prime(k), ..., prime(k+10).
%H A127340 Syed Iddi Hasan, <a href="/A127340/b127340.txt">Table of n, a(n) for n = 1..10000</a>
%t A127340 a = {}; Do[If[PrimeQ[Sum[Prime[x + n], {n, 0, 10}]], AppendTo[a, Sum[Prime[x + n], {n, 0, 10}]]], {x, 1, 500}]; a
%t A127340 Select[Total/@Partition[Prime[Range[200]],11,1],PrimeQ] (* _Harvey P. Dale_, Jul 16 2012 *)
%o A127340 (PARI) {m=125;k=11;for(n=0,m-1,a=sum(j=1,k,prime(n+j));if(isprime(a),print1(a,",")))} \\ _Klaus Brockhaus_, Jan 13 2007
%o A127340 (PARI) {m=126;k=11;for(n=1,m,a=abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1));if(isprime(a),print1(a,",")))} \\ _Klaus Brockhaus_, Jan 13 2007
%Y A127340 Cf. A127338, A034962, A034965, A082246, A082251, A127341.
%K A127340 nonn
%O A127340 1,1
%A A127340 _Artur Jasinski_, Jan 11 2007
%E A127340 Edited by _Klaus Brockhaus_, Jan 13 2007