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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 (list; graph; refs; listen; history; text; internal format)
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) 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
CROSSREFS
Sequence in context: A132917 A139652 A126979 * A140033 A142182 A105981
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jan 13 2007
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)