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
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)
Programs
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Maple
seq(numtheory:-pi(mul(ithprime(i),i=1..n)),n=0..10); # Robert Israel, Aug 25 2014
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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 *) -
PARI
t=1;forprime(p=2,66,print1(primepi(t),", ");t*=p); \\ Joerg Arndt, Aug 25 2014
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Sage
[prime_pi(sloane.A002110(n)) for n in range (14)] # Giuseppe Coppoletta, Mar 02 2015
Formula
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