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A127337 Numbers that are the sum of 10 consecutive primes. 15
129, 158, 192, 228, 264, 300, 340, 382, 424, 468, 510, 552, 594, 636, 682, 732, 780, 824, 870, 912, 954, 1008, 1060, 1114, 1164, 1216, 1266, 1320, 1376, 1434, 1494, 1546, 1596, 1650, 1704, 1752, 1800, 1854, 1914, 1974, 2030, 2084, 2142, 2192, 2250, 2310 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = absolute value of coefficient of x^9 of the polynomial Product_{j=0..9} (x - prime(n+j)) of degree 10; the roots of this polynomial are prime(n), ..., prime(n+9).

LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000

MATHEMATICA

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a

Table[Plus@@Prime[Range[n, n + 9]], {n, 50}] (* Alonso del Arte, Feb 15 2011 *)

ListConvolve[ConstantArray[1, 10], Prime[Range[50]]]

Total/@Partition[Prime[Range[60]], 10, 1] (* Harvey P. Dale, Jan 31 2013 *)

PROG

(PARI) {m=46; k=10; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007

(PARI) {m=46; k=10; 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..9] ]: n in [1..90] ]; // Vincenzo Librandi, Apr 03 2011

CROSSREFS

Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127338, A127339.

Sequence in context: A025324 A230092 A060878 * A185347 A034072 A235879

Adjacent sequences:  A127334 A127335 A127336 * A127338 A127339 A127340

KEYWORD

nonn

AUTHOR

Artur Jasinski, Jan 11 2007

EXTENSIONS

Edited by Klaus Brockhaus, Jan 13 2007

STATUS

approved

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Last modified April 25 00:32 EDT 2017. Contains 285346 sequences.