A099824 a(n) = Sum of the first 10^n primes.

2, 129, 24133, 3682913, 496165411, 62260698721, 7472966967499, 870530414842019, 99262851056183695, 11138479445180240497, 1234379338586942892505, 135436174616790289414111, 14738971133550183905879827, 1593061976858155930556059673, 171191473337951767580578821529

Offset

0,1

Links

David Baugh, Table of n, a(n) for n = 0..23 [terms a(0)-a(17) from Marc Deleglise; terms a(18)-a(21) from Kim Walisch]

Cino Hilliard, SumPrimes, June 2008. [broken link]

Formula

a(n) = Sum_{i=1..10^n} A000040(i). - José de Jesús Camacho Medina, Dec 27 2014 (corrected by Joerg Arndt, Jan 05 2015)

Example

For n=1, the sum of the first 10^1 = 10 primes is 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129, so a(1) = 129. - Michael B. Porter, Aug 08 2016

Mathematica

NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; k = p = 1; s = 0; Do[ While[p = NextPrim[p]; s = s + p; k < 10^n, k++ ]; k++; Print[s], {n, 0, 8}]
Table[Sum[Prime[i], {i, 10^n}], {n, 0, 5}] (* José de Jesús Camacho Medina, Dec 27 2014 *)

Prog

(PARI) vecA099824(n)={ my(s, c, k=1, L:list); L=List();
forprime(m=2, prime(10^n), s+=m; c++; if(c==k, listput(L, s); k*=10));
return(vector(#L, i, L[i]))} \\ R. J. Cano, Aug 12 2016

Crossrefs

Cf. A000040, A006988, A007504, A099825, A099826.

Sequence in context: A216358 A361890 A294274 * A351916 A300292 A259109

Adjacent sequences: A099821 A099822 A099823 * A099825 A099826 A099827

Keyword

nonn

Author

Robert G. Wilson v, Oct 25 2004

Extensions

a(9) from Hans Havermann, May 06 2005

a(10) from Cino Hilliard, Apr 28 2006

a(11) from Cino Hilliard, Oct 03 2006

a(12)-a(13) from Hiroaki Yamanouchi, Jul 06 2014

a(11) corrected by Marc Deleglise, Apr 03 2016

a(14)-a(17) from Marc Deleglise, Apr 03 2016

a(18)-a(20) from Kim Walisch, Jun 05 2016

a(21) from Kim Walisch, Jun 11 2016

a(22) from David Baugh using Kim Walisch's primesum program, Jun 21 2016

a(23) from David Baugh using Kim Walisch's primesum program, Sep 26 2016

Status

approved