|
|
A131740
|
|
a(n) = sum of n successive primes after the n-th prime.
|
|
2
|
|
|
3, 12, 31, 60, 101, 156, 223, 304, 401, 510, 631, 766, 923, 1090, 1265, 1470, 1687, 1926, 2179, 2448, 2735, 3040, 3353, 3698, 4057, 4428, 4817, 5230, 5661, 6106, 6555, 7042, 7535, 8064, 8611, 9172, 9755, 10354, 10973, 11610, 12271, 12954, 13645
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The prime number theorem implies that, if q(n) = sum of first n primes, then a(n)/q(n) -> 3 as n -> oo. - N. J. A. Sloane, Oct 04 2007
|
|
LINKS
|
|
|
EXAMPLE
|
a(4)=60 because 11, 13, 17 and 19 follow the 4th prime, 7, and 11 + 13 + 17 + 19 = 60.
|
|
MAPLE
|
a:=proc(n) options operator, arrow; add(ithprime(j), j=n+1..2*n) end proc: seq(a(n), n=1..45); # Emeric Deutsch, Oct 20 2007
|
|
MATHEMATICA
|
Table[Total[Prime[Range[n+1, 2n]]], {n, 50}] (* Harvey P. Dale, Apr 13 2018 *)
|
|
PROG
|
(PARI) a(n)=my(t=0); for(i=1, n, t=t+prime(n+i)); t \\ Anders Hellström, Sep 16 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|