OFFSET
1,1
COMMENTS
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).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ 8n log n. - Charles R Greathouse IV, Apr 19 2015
MAPLE
S:= [0, op(ListTools:-PartialSums(select(isprime, [2, seq(i, i=3..1000, 2)])))]:
S[9..-1]-S[1..-9]; # Robert Israel, Nov 27 2017
MATHEMATICA
a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 7}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]], 8, 1] (* Harvey P. Dale, Sep 10 2019 *)
PROG
(PARI) {m=48; k=8; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007
(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
(PARI) a(n)=my(p=prime(n)); p+sum(i=2, 8, p=nextprime(p+1)) \\ Charles R Greathouse IV, Apr 19 2015
(Magma) [&+[ NthPrime(n+k): k in [0..7] ]: n in [1..90] ]; // Vincenzo Librandi, Apr 03 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jan 13 2007
STATUS
approved