A127333 - OEIS

A127333

Numbers that are the sum of 6 consecutive primes.

41, 56, 72, 90, 112, 132, 156, 180, 204, 228, 252, 280, 304, 330, 358, 384, 410, 434, 462, 492, 522, 552, 580, 606, 630, 660, 690, 724, 756, 796, 834, 864, 896, 926, 960, 990, 1020, 1054, 1084, 1114, 1140, 1172, 1214, 1250, 1286, 1322, 1362, 1392, 1420

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OFFSET

1,1

COMMENTS

a(n) is the absolute value of coefficient of x^5 of the polynomial Prod_{j=0,5}(x-prime(n+j)) of degree 6; the zeros of this polynomial are prime(n), ..., prime(n+5).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 5}]], {x, 1, 50}]; a

Total/@Partition[Prime[Range[60]], 6, 1] (* Harvey P. Dale, Mar 12 2015 *)

PROG

(PARI) {m=50; k=6; for(n=0, m-1, print1(a=sum(j=1, k, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 12 2007

(PARI) {m=50; k=6; for(n=1, m, print1(abs(polcoeff(prod(j=0, k-1, (x-prime(n+j))), k-1)), ", "))} \\ Klaus Brockhaus, Jan 12 2007

(Magma) [&+[ NthPrime(n+k): k in [0..5] ]: n in [1..80] ]; /* Vincenzo Librandi, Apr 03 2011 */

CROSSREFS