|
|
A127338
|
|
Numbers that are the sum of 11 consecutive primes.
|
|
13
|
|
|
160, 195, 233, 271, 311, 353, 399, 443, 491, 539, 583, 631, 677, 725, 779, 833, 883, 931, 979, 1025, 1081, 1139, 1197, 1253, 1313, 1367, 1423, 1483, 1543, 1607, 1673, 1727, 1787, 1843, 1901, 1951, 2011, 2077, 2141, 2203, 2263, 2323, 2383, 2443, 2507
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
a(n) = absolute value of coefficient of x^10 of the polynomial Product_{j=0..10} (x - prime(n+j)) of degree 11; the roots of this polynomial are prime(n), ..., prime(n+10).
|
|
LINKS
|
|
|
MATHEMATICA
|
f[n_] := Sum[Prime[n + i], {i, 0, 10}]; Array[f, 45]
|
|
PROG
|
(PARI) {m=45; k=11; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007
(PARI) {m=45; k=11; 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..10] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011
|
|
CROSSREFS
|
Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127339, A127340.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|