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

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

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

Crossrefs

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127339, A127340.

Programs

Magma

[&+[ NthPrime(n+k): k in [0..10] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011

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 *)

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

Extensions

Edited by Klaus Brockhaus, Jan 13 2007