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A127336 Numbers that are the sum of 9 consecutive primes. 11
100, 127, 155, 187, 221, 253, 287, 323, 363, 401, 439, 479, 515, 553, 593, 635, 679, 721, 763, 803, 841, 881, 929, 977, 1025, 1067, 1115, 1163, 1213, 1267, 1321, 1367, 1415, 1459, 1511, 1555, 1601, 1643, 1691, 1747, 1801, 1851, 1903, 1951, 1999, 2053 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = absolute value of coefficient of x^8 of the polynomial Product_{j=0..8}(x - prime(n+j)) of degree 9; the roots of this polynomial are prime(n), ..., prime(n+8).

LINKS

Table of n, a(n) for n=1..46.

MATHEMATICA

A127336 = {}; Do[AppendTo[A127336, Sum[Prime[x + n], {n, 0, 8}]], {x, 1, 50}]; A127336 (* Artur Jasinski, Jan 11 2007 *)

Table[Plus@@Prime[Range[n, n + 8]], {n, 50}] (* Alonso del Arte, Aug 27 2013 *)

PROG

(PARI) {m=46; k=9; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007

{m=46; k=9; for(n=1, m, print1(abs(polcoeff(prod(j=0, k-1, (x-prime(n+j))), k-1)), ", "))} \\ Klaus Brockhaus, Jan 13 2007

(MAGMA) [&+[ NthPrime(n+k): k in [0..8] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011

(Python)

from sympy import prime

def a(x): return sum([prime(x + n) for n in range(0, 9)])

print[a(i) for i in xrange(1, 50)] # Indranil Ghosh, Mar 18 2017

CROSSREFS

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127337, A127338, A127339, A082251, A228200.

Sequence in context: A066139 A037139 A109881 * A045211 A244391 A108551

Adjacent sequences:  A127333 A127334 A127335 * A127337 A127338 A127339

KEYWORD

nonn,easy,changed

AUTHOR

Artur Jasinski, Jan 11 2007

EXTENSIONS

Edited by Klaus Brockhaus, Jan 13 2007

STATUS

approved

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Last modified March 27 04:41 EDT 2017. Contains 284144 sequences.