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A127337
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Numbers that are the sum of 10 consecutive primes.
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9
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = absolute value of coefficient of x^9 of the polynomial Prod_{j=0,9}(x-prime(n+j)) of degree 10; the roots of this polynomial are prime(n), ..., prime(n+9).
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MATHEMATICA
| a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 9}]], {x, 1, 50}]; a (* Jasinski *)
Table[Plus@@Prime[Range[n, n + 9]], {n, 50}] (* From Alonso del Arte, Feb 15 2011 *)
ListConvolve[ConstantArray[1, 10], Prime[Range[50]]]
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PROG
| (PARI) 1. {m=46; k=10; for(n=1, m, print1(a=sum(j=0, k-1, prime(n+j)), ", "))} 2. {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
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CROSSREFS
| Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127338, A127339.
Sequence in context: A025332 A025324 A060878 * A185347 A034072 A157951
Adjacent sequences: A127334 A127335 A127336 * A127338 A127339 A127340
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Jan 11 2007
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EXTENSIONS
| Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 13 2007
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