A127340 Primes that are the sum of 11 consecutive primes.

233, 271, 311, 353, 443, 491, 631, 677, 883, 1367, 1423, 1483, 1543, 1607, 1787, 1901, 1951, 2011, 2141, 2203, 2383, 3253, 3469, 3541, 3617, 3691, 3967, 4159, 4229, 4297, 4943, 5009, 5483, 5657, 5741, 5903, 5981, 6553, 6871, 6991, 7057, 7121, 7187, 7873

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

Primes in A127338.

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).

Links

• Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A127338, A034962, A034965, A082246, A082251, A127341.

Programs

Mathematica

a = {}; Do[If[PrimeQ[Sum[Prime[x + n], {n, 0, 10}]], AppendTo[a, Sum[Prime[x + n], {n, 0, 10}]]], {x, 1, 500}]; a
Select[Total/@Partition[Prime[Range[200]],11,1],PrimeQ] (* Harvey P. Dale, Jul 16 2012 *)

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

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

Extensions

Edited by Klaus Brockhaus, Jan 13 2007