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