

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
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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, k1, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007
(PARI) {m=46; k=10; for(n=1, m, print1(abs(polcoeff(prod(j=0, k1, (xprime(n+j))), k1)), ", "))} \\ 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



