A046731 a(n) = sum of primes < 10^n.
0, 17, 1060, 76127, 5736396, 454396537, 37550402023, 3203324994356, 279209790387276, 24739512092254535, 2220822432581729238, 201467077743744681014, 18435588552550705911377, 1699246443377779418889494, 157589260710736940541561021, 14692398516908006398225702366
Offset: 0
Examples
The primes less than 10 give 2+3+5+7 = 17.
Links
- Lorenzo Pieri, Table of n, a(n) for n = 0..26 [terms a(0)-a(20) from Marc Deleglise; terms a(21)-a(23) from Kim Walisch; terms a(24)-a(25) from David Baugh]
- M. Deleglise and J. Rivat, Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp., 65 (1996), 235-245.
- Cino Hilliard, GmpDemo Sumprimes.
- Cino Hilliard, Achim Sieve Gmp Sumprimes.
- Cino Hilliard, Achim Multi-Prec add Sumprimes.
- Kim Walisch, primesum program.
Crossrefs
Cf. A034387.
Programs
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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 *) -
PARI
a(n) = my(s=0); forprime(p=1, 10^n, s += p); s; \\ Michel Marcus, Jan 14 2015
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Perl
use ntheory ":all"; say "$ ",sum_primes(10**$) for 0..15; # Dana Jacobsen, May 04 2017
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
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 b-file. This has now been corrected. - N. J. A. Sloane, Nov 23 2007
Two new values from Marc Deleglise, May 21 2008 - see the b-file.
a(21) from Marc Deleglise, Jun 29 2008 - see the b-file.
Nov 15 2011: Marc Deleglise has withdrawn his value for a(21).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
a(26) from Kim Walisch, May 25 2022, added by Lorenzo Pieri
Comments