A181671 Number of Ramanujan primes less than 10^n.

1, 10, 72, 559, 4459, 36960, 316066, 2760321, 24491666, 220098288, 1998400235, 18299775876, 168773875190, 1566017986235, 14606736768049, 136860923837558, 1287462389890262

Offset: 1

Author

T. D. Noe, Nov 18 2010

Keywords

• nonn
• more

Crossrefs

Cf. A104272 (Ramanujan primes).

Cf. A190502 (Number of Ramanujan primes <= 2^n).

Programs

Mathematica

nn=50000; t=Table[0,{nn}]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s
				

Perl

use ntheory ":all"; for my $e (1..9) { say "$e ",scalar(@{ramanujan_primes(10**$e)}); } # Dana Jacobsen, May 10 2015
# To control memory use at cost of speed:

Perl

use ntheory ":all"; my($n,$inc,$start,$sum)=(1e10,1e9,0,0); while ($start < $n) { $sum += scalar(@{ramanujan_primes($start,$start+$inc-1)}); $start += $inc; } say $sum; # Dana Jacobsen, May 10 2015

Perl

use ntheory ":all"; say ramanujan_prime_count(10**$) for 1..11; # _Dana Jacobsen, Jan 03 2016

Extensions

a(10)-a(11) from Dana Jacobsen, Dec 29 2014

a(12) from Dana Jacobsen, Sep 08 2015

a(13)-a(14) from Dana Jacobsen, Jan 03 2016

a(15)-a(17) from Dana Jacobsen, Apr 26 2017