A000849 Number of primes <= product of first n primes, A002110(n).

0, 1, 3, 10, 46, 343, 3248, 42331, 646029, 12283531, 300369796, 8028643010, 259488750744, 9414916809095, 362597750396740, 15397728527812858, 742238179058722891, 40068968501510691894, 2251262473052300960826, 139566579945945392719413

Offset

0,3

Links

David Baugh, Table of n, a(n) for n = 0..19 (terms n = 18..19 found using Kim Walisch's primecount program).

R. Mestrovic, An elementary proof of an estimate for a number of primes less than the product of the first n primes, arXiv:1211.4571 [math.NT], 2012.

C. D. Pruitt, A Theorem & Proof on the Density of Primes Utilizing Primorials

Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Formula

a(n) = A000720(A002110(n)). - Michel Marcus, Aug 25 2014

Maple

seq(numtheory:-pi(mul(ithprime(i), i=1..n)), n=0..10); # Robert Israel, Aug 25 2014

Mathematica

a=1; Table[a=a*Prime[n]; PrimePi[a], {n, 12}]
Join[{0}, PrimePi/@FoldList[Times, Prime[Range[12]]]] (* Harvey P. Dale, Jan 28 2019 *)

Prog

(PARI) t=1; forprime(p=2, 66, print1(primepi(t), ", "); t*=p); \\ Joerg Arndt, Aug 25 2014
(Sage) [prime_pi(sloane.A002110(n)) for n in range (14)] # Giuseppe Coppoletta, Mar 02 2015

Crossrefs

Cf. A000720, A002110, A003604.

Sequence in context: A345132 A020008 A167999 * A092429 A218919 A346188

Adjacent sequences: A000846 A000847 A000848 * A000850 A000851 A000852

Keyword

nonn,hard

Author

James D. Ausfahl, gandalf(AT)hrn.office.ssi.net

Extensions

More terms from David W. Wilson

a(10)-a(13) from Paul Zimmermann

a(14)-a(15) from Donovan Johnson, Mar 01 2010

a(16)-a(17) from Henri Lifchitz, Aug 25 2014

a(18)-a(19) from David Baugh, Sep 29 2020

Status

approved