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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, 2374 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the 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 FORMULA a(n) = A127336(n)+A000040(n+9). - R. J. Mathar, Apr 24 2023 MAPLE A127337 := proc(n) local i ; add(ithprime(n+i), i=0..9) ; end proc: seq(A127337(n), n=1..30) ; # R. J. Mathar, Apr 24 2023 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 (Python) from sympy import prime def a(n): return sum(prime(n + i) for i in range(10)) print([a(n) for n in range(1, 48)]) # Michael S. Branicky, Dec 09 2021 (Python) # faster version for generating initial segment of sequence from sympy import nextprime def aupton(terms): alst, plst = [], [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] for n in range(terms): alst.append(sum(plst)) plst = plst[1:] + [nextprime(plst[-1])] return alst print(aupton(47)) # Michael S. Branicky, Dec 09 2021 CROSSREFS Cf. A011974, A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127338, A127339. Sequence in context: A025324 A230092 A060878 * A185347 A034072 A178228 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 September 10 23:44 EDT 2024. Contains 375795 sequences. (Running on oeis4.)