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A127335 Numbers that are the sum of 8 successive primes. 14
77, 98, 124, 150, 180, 210, 240, 270, 304, 340, 372, 408, 442, 474, 510, 546, 582, 620, 660, 696, 732, 768, 802, 846, 888, 928, 966, 1012, 1056, 1104, 1154, 1194, 1236, 1278, 1320, 1362, 1404, 1444, 1480, 1524, 1574, 1622, 1670, 1712, 1758, 1802, 1854, 1900 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A269809 A064902 A247682 * A193570 A154534 A235867
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 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)