

A046731


a(n) = sum of primes < 10^n.


18



0, 17, 1060, 76127, 5736396, 454396537, 37550402023, 3203324994356, 279209790387276, 24739512092254535, 2220822432581729238, 201467077743744681014, 18435588552550705911377, 1699246443377779418889494, 157589260710736940541561021, 14692398516908006398225702366
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OFFSET

0,2


COMMENTS

a(21) was already correctly computed by Marc Deleglise in 2009 but in 2011 he withdrew his result because his verification failed.  Kim Walisch, Jun 06 2016


LINKS

David Baugh, Table of n, a(n) for n = 0..25 [terms a(0)a(20) from Marc Deleglise; terms a(21)a(23) from Kim Walisch]
M. Deleglise and J. Rivat, Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp., 65 (1996), 235245.
Cino Hilliard, GmpDemo Sumprimes.
Cino Hilliard, Achim Sieve Gmp Sumprimes.
Cino Hilliard, Achim MultiPrec add Sumprimes.
Kim Walisch, primesum program.


FORMULA

a(n) is about 100^n/(n log 100).  Charles R Greathouse IV, Jan 29 2013
a(n) = Sum_{i=2..10^n} A061397(i).  José de Jesús Camacho Medina, Aug 08 2016


EXAMPLE

The primes less than 10 give 2+3+5+7 = 17.


MATHEMATICA

Join[{0, s = 17}, Table[Do[If[PrimeQ[i], s += i], {i, 10^n + 1, 10^(n + 1), 2}]; s, {n, 7}]] (* Jayanta Basu, Jun 28 2013 *)
Table[Sum[Prime[i], {i, PrimePi[10^n]}], {n, 0, 7}] (* Kim Walisch, Dec 21 2017 *)


PROG

(PARI) a(n) = my(s=0); forprime(p=1, 10^n, s += p); s; \\ Michel Marcus, Jan 14 2015
(Perl) use ntheory ":all"; say "$_ ", sum_primes(10**$_) for 0..15; # Dana Jacobsen, May 04 2017


CROSSREFS

Cf. A034387.
Sequence in context: A221343 A221376 A077645 * A221268 A179157 A130449
Adjacent sequences: A046728 A046729 A046730 * A046732 A046733 A046734


KEYWORD

nonn,nice


AUTHOR

Enoch Haga


EXTENSIONS

Corrected and extended by Jud McCranie
a(12) and a(13) from Cino Hilliard, Aug 14 2006.
New value for a(13) from Cino Hilliard, Oct 24 2007
There was indeed an error in a(13) both in the entry here and in the bfile. This has now been corrected.  N. J. A. Sloane, Nov 23 2007
Two new values from Marc Deleglise, May 21 2008  see the bfile.
a(21) from Marc Deleglise, Jun 29 2008  see the bfile.
Nov 15 2011: Marc Deleglise has withdrawn his value for a(21).
a(21)a(22) from Kim Walisch, Jun 06 2016
a(23) from Kim Walisch, Jun 11 2016
a(24) from David Baugh using Kim Walisch's primesum program, Jun 17 2016
a(25) from David Baugh using Kim Walisch's primesum program, Oct 16 2016


STATUS

approved



