A127336 Numbers that are the sum of 9 consecutive primes.

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

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.

Formula

a(n) = A127335(n)+A000040(n+8). - R. J. Mathar, Apr 24 2023

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 *)
Total/@Partition[Prime[Range[60]], 9, 1] (* Harvey P. Dale, Nov 18 2020 *)

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(9)])
print([a(i) for i in range(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: A109881 A292275 A295161 * A045211 A244391 A108551

Adjacent sequences: A127333 A127334 A127335 * A127337 A127338 A127339

Keyword

nonn,easy

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

Status

approved