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
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 11 2007
EXTENSIONS
Edited by Klaus Brockhaus, Jan 13 2007
STATUS
approved