|
|
A127333
|
|
Numbers that are the sum of 6 consecutive primes.
|
|
13
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|