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%I #28 Sep 08 2022 08:45:29
%S 160,195,233,271,311,353,399,443,491,539,583,631,677,725,779,833,883,
%T 931,979,1025,1081,1139,1197,1253,1313,1367,1423,1483,1543,1607,1673,
%U 1727,1787,1843,1901,1951,2011,2077,2141,2203,2263,2323,2383,2443,2507
%N Numbers that are the sum of 11 consecutive primes.
%C a(n) = absolute value of coefficient of x^10 of the polynomial Product_{j=0..10} (x - prime(n+j)) of degree 11; the roots of this polynomial are prime(n), ..., prime(n+10).
%H Charles R Greathouse IV, <a href="/A127338/b127338.txt">Table of n, a(n) for n = 1..10000</a>
%t f[n_] := Sum[Prime[n + i], {i, 0, 10}]; Array[f, 45]
%t Plus @@@ Partition[ Prime@ Range@ 55, 11, 1] (* _Robert G. Wilson v_, Jan 13 2011 *)
%o (PARI) {m=45;k=11;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 13 2007
%o (PARI) {m=45;k=11;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ _Klaus Brockhaus_, Jan 13 2007
%o (Magma) [&+[ NthPrime(n+k): k in [0..10] ]: n in [1..70] ]; // _Vincenzo Librandi_, Apr 03 2011
%Y Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127339, A127340.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 11 2007
%E Edited by _Klaus Brockhaus_, Jan 13 2007
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