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A127340
Primes that are the sum of 11 consecutive primes.
13
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
1,1
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jan 13 2007
STATUS
approved