

A131740


a(n) = sum of n successive primes after the nth 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
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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

Harvey P. Dale, Table of n, a(n) for n = 1..1000


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[Sum[Prime[n + i], {i, 1, n}], {n, 1, 50}] (* Stefan Steinerberger, Oct 07 2007 *)
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

Cf. A007504.
Sequence in context: A293656 A131936 A009135 * A037237 A005718 A199231
Adjacent sequences: A131737 A131738 A131739 * A131741 A131742 A131743


KEYWORD

nonn


AUTHOR

G. L. Honaker, Jr., Oct 03 2007


EXTENSIONS

More terms from Stefan Steinerberger, Oct 07 2007
More terms from Emeric Deutsch, Oct 20 2007


STATUS

approved



