login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers that are the sum of 11 consecutive primes.
13

%I #28 Sep 08 2022 08:45:29

%S 160,195,233,271,311,353,399,443,491,539,583,631,677,725,779,833,883,

%T 931,979,1025,1081,1139,1197,1253,1313,1367,1423,1483,1543,1607,1673,

%U 1727,1787,1843,1901,1951,2011,2077,2141,2203,2263,2323,2383,2443,2507

%N Numbers that are the sum of 11 consecutive primes.

%C 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).

%H Charles R Greathouse IV, <a href="/A127338/b127338.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_] := Sum[Prime[n + i], {i, 0, 10}]; Array[f, 45]

%t Plus @@@ Partition[ Prime@ Range@ 55, 11, 1] (* _Robert G. Wilson v_, Jan 13 2011 *)

%o (PARI) {m=45;k=11;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ _Klaus Brockhaus_, Jan 13 2007

%o (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

%o (Magma) [&+[ NthPrime(n+k): k in [0..10] ]: n in [1..70] ]; // _Vincenzo Librandi_, Apr 03 2011

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

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 11 2007

%E Edited by _Klaus Brockhaus_, Jan 13 2007