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

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

Cf. A011974, A001043, A034961, A034963, A034964, A127334, A127335, A127336, A127337, A127338, A127339.

Sequence in context: A282353 A118636 A116345 * A262722 A172406 A161613

Adjacent sequences: A127330 A127331 A127332 * A127334 A127335 A127336

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 12 2007

Status

approved