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A127334 Numbers that are the sum of 7 consecutive primes. 11
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A368615 A184074 A281824 * A275702 A306115 A039430
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jan 13 2007
STATUS
approved

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Last modified April 13 18:51 EDT 2024. Contains 371644 sequences. (Running on oeis4.)