A127337 Numbers that are the sum of 10 consecutive primes.

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

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