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A127335 Numbers that are the sum of 8 successive primes. 13
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) = 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

PROG

(PARI) 1. {m=48; k=8; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} 2. {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

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127336, A127337, A127338, A127339.

Sequence in context: A269809 A064902 A247682 * A193570 A154534 A235867

Adjacent sequences:  A127332 A127333 A127334 * A127336 A127337 A127338

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jan 11 2007

EXTENSIONS

Edited by Klaus Brockhaus, Jan 13 2007

STATUS

approved

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Last modified February 21 15:58 EST 2018. Contains 299414 sequences. (Running on oeis4.)