A127338 Numbers that are the sum of 11 consecutive primes.

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

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Mathematica

f[n_] := Sum[Prime[n + i], {i, 0, 10}]; Array[f, 45]
Plus @@@ Partition[ Prime@ Range@ 55, 11, 1] (* Robert G. Wilson v, Jan 13 2011 *)

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.

Sequence in context: A171225 A290463 A367206 * A138854 A133530 A278129

Adjacent sequences: A127335 A127336 A127337 * A127339 A127340 A127341

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

Status

approved