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A127340
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Primes that are the sum of 11 consecutive primes.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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MATHEMATICA
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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 *)
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PROG
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(PARI) 1. {m=125; k=11; for(n=0, m-1, a=sum(j=1, k, prime(n+j)); if(isprime(a), print1(a, ", ")))} 2. {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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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