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%I #34 Sep 08 2022 08:45:29
%S 41,56,72,90,112,132,156,180,204,228,252,280,304,330,358,384,410,434,
%T 462,492,522,552,580,606,630,660,690,724,756,796,834,864,896,926,960,
%U 990,1020,1054,1084,1114,1140,1172,1214,1250,1286,1322,1362,1392,1420
%N Numbers that are the sum of 6 consecutive primes.
%C a(n) is the absolute value of coefficient of x^5 of the polynomial Prod_{j=0,5}(x-prime(n+j)) of degree 6; the zeros of this polynomial are prime(n), ..., prime(n+5).
%H Harvey P. Dale, <a href="/A127333/b127333.txt">Table of n, a(n) for n = 1..1000</a>
%t a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 5}]], {x, 1, 50}]; a
%t Total/@Partition[Prime[Range[60]],6,1] (* _Harvey P. Dale_, Mar 12 2015 *)
%o (PARI) {m=50;k=6;for(n=0,m-1,print1(a=sum(j=1,k,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 12 2007
%o (PARI) {m=50;k=6;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ _Klaus Brockhaus_, Jan 12 2007
%o (Magma) [&+[ NthPrime(n+k): k in [0..5] ]: n in [1..80] ]; /* _Vincenzo Librandi_, Apr 03 2011 */
%Y Cf. A011974, A001043, A034961, A034963, A034964, A127334, A127335, A127336, A127337, A127338, A127339.
%K nonn
%O 1,1
%A _Artur Jasinski_, Jan 11 2007
%E Edited by _Klaus Brockhaus_, Jan 12 2007
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