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

1,1

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).

Links

Table of n, a(n) for n=1..45.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A159809 A345551 A051371 * A345805 A142121 A142274

Adjacent sequences: A127336 A127337 A127338 * A127340 A127341 A127342

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

Status

approved