A127334 Numbers that are the sum of 7 consecutive primes.

58, 75, 95, 119, 143, 169, 197, 223, 251, 281, 311, 341, 371, 401, 431, 463, 493, 523, 559, 593, 625, 659, 689, 719, 757, 791, 827, 863, 905, 947, 991, 1027, 1063, 1099, 1139, 1171, 1211, 1247, 1281, 1313, 1351, 1395, 1441, 1479, 1519, 1561, 1603, 1643

Offset

1,1

Comments

a(n) = absolute value of coefficient of x^6 of the polynomial Product_{j=0..6} (x - prime(n+j)) of degree 7; the roots of this polynomial are prime(n), ..., prime(n+6).

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

Maple

seq(add(ithprime(i), i=n..6+n), n=1..50); # Muniru A Asiru, Apr 16 2018

Mathematica

a = {}; Do[AppendTo[a, Sum[Prime[x + n], {n, 0, 6}]], {x, 1, 50}]; a
Total/@Partition[Prime[Range[60]], 7, 1] (* Harvey P. Dale, May 14 2023 *)

Prog

(PARI) {m=48; k=7; for(n=0, m-1, print1(a=sum(j=1, k, prime(n+j)), ", "))} \\ Klaus Brockhaus, Jan 13 2007
(PARI) {m=48; k=7; for(n=1, m, print1(abs(polcoeff(prod(j=0, k-1, (x-prime(n+j))), k-1)), ", "))} \\ Klaus Brockhaus, Jan 13 2007
(Sage)
BB = primes_first_n(62)
L = []
for i in range(55):
    L.append(sum(BB[i+j] for j in range(7)))
L
# Zerinvary Lajos, May 14 2007
(Magma) [&+[ NthPrime(n+k): k in [0..6] ]: n in [1..70] ]; // Vincenzo Librandi, Apr 03 2011
(Python)
from sympy import prime
def a(x): return sum(prime(x + n) for n in range(7))
print([a(i) for i in range(1, 50)]) # Indranil Ghosh, Mar 18 2017
(GAP) P:=Filtered([1..1000], IsPrime);; List([0..50], n->Sum([1+n..7+n], i->P[i])); # Muniru A Asiru, Apr 16 2018

Crossrefs

Cf. A001043, A011974, A034961, A034963, A034964, A082246, A127333, A127335, A127336, A127337, A127338, A127339.

Sequence in context: A368615 A184074 A281824 * A275702 A306115 A039430

Adjacent sequences: A127331 A127332 A127333 * A127335 A127336 A127337

Keyword

nonn

Author

Artur Jasinski, Jan 11 2007

Extensions

Edited by Klaus Brockhaus, Jan 13 2007

Status

approved