A127339 Numbers that are the sum of 12 consecutive primes.

197, 236, 276, 318, 364, 412, 460, 510, 562, 612, 662, 714, 766, 822, 880, 936, 990, 1040, 1092, 1152, 1212, 1276, 1336, 1402, 1464, 1524, 1586, 1650, 1716, 1786, 1854, 1918, 1980, 2040, 2100, 2162, 2234, 2304, 2370, 2436, 2502, 2564, 2634, 2700, 2770

Offset: 1

Author

Artur Jasinski, Jan 11 2007

Keywords

• nonn

Comments

a(n) = absolute value of coefficient of x^11 of the polynomial Product_{j=0..11} (x - prime(n+j)) of degree 12; the roots of this polynomial are prime(n), ..., prime(n+11).

Crossrefs

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127338.

Programs

Magma

[&+[ NthPrime(n+k): k in [0..11] ]: n in [1..100] ]; // Vincenzo Librandi, Apr 03 2011

Mathematica

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 11}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]],12,1] (* Harvey P. Dale, May 05 2018 *)

PARI

{m=45;k=12;for(n=1,m,print1(a=sum(j=0,k-1,prime(n+j)),","))} \\ Klaus Brockhaus, Jan 13 2007

PARI

{m=45;k=12;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