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A127335 Numbers that are the sum of 8 successive primes.

%I A127335 #28 Sep 08 2022 08:45:29
%S A127335 77,98,124,150,180,210,240,270,304,340,372,408,442,474,510,546,582,
%T A127335 620,660,696,732,768,802,846,888,928,966,1012,1056,1104,1154,1194,
%U A127335 1236,1278,1320,1362,1404,1444,1480,1524,1574,1622,1670,1712,1758,1802,1854,1900
%N A127335 Numbers that are the sum of 8 successive primes.
%C A127335 a(n) is the absolute value of coefficient of x^7 of the polynomial Prod_{j=0,7}(x-prime(n+j)) of degree 8; the roots of this polynomial are prime(n), ..., prime(n+7).
%H A127335 Robert Israel, <a href="/A127335/b127335.txt">Table of n, a(n) for n = 1..10000</a>
%F A127335 a(n) ~ 8n log n. - _Charles R Greathouse IV_, Apr 19 2015
%p A127335 S:= [0,op(ListTools:-PartialSums(select(isprime, [2,seq(i,i=3..1000,2)])))]:
%p A127335 S[9..-1]-S[1..-9]; # _Robert Israel_, Nov 27 2017
%t A127335 a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 7}]], {x, 1, 50}]; a
%t A127335 Total/@Partition[Prime[Range[60]],8,1] (* _Harvey P. Dale_, Sep 10 2019 *)
%o A127335 (PARI) {m=48;k=8;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 13 2007
%o A127335 (PARI) {m=48;k=8;for(n=1,m,print1(abs(polcoeff(prod(j=0,k-1,(x-prime(n+j))),k-1)),","))} \\ _Klaus Brockhaus_, Jan 13 2007
%o A127335 (PARI) a(n)=my(p=prime(n));p+sum(i=2,8,p=nextprime(p+1)) \\ _Charles R Greathouse IV_, Apr 19 2015
%o A127335 (Magma) [&+[ NthPrime(n+k): k in [0..7] ]: n in [1..90] ]; // _Vincenzo Librandi_, Apr 03 2011
%Y A127335 Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127336, A127337, A127338, A127339.
%K A127335 nonn
%O A127335 1,1
%A A127335 _Artur Jasinski_, Jan 11 2007
%E A127335 Edited by _Klaus Brockhaus_, Jan 13 2007