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A181671 Number of Ramanujan primes less than 10^n.

%I A181671 #31 Apr 26 2017 22:27:34
%S A181671 1,10,72,559,4459,36960,316066,2760321,24491666,220098288,1998400235,
%T A181671 18299775876,168773875190,1566017986235,14606736768049,
%U A181671 136860923837558,1287462389890262
%N A181671 Number of Ramanujan primes less than 10^n.
%t A181671 nn=50000; t=Table[0,{nn}]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s<nn, t[[s+1]]=k], {k, Prime[3*nn]}]; t=t+1; i=1; Table[While[t[[i]]<10^n, i++]; i-1, {n,Floor[Log[10,t[[-1]]]]}]
%o A181671 (Perl) use ntheory ":all"; for my $e (1..9) { say "$e ",scalar(@{ramanujan_primes(10**$e)}); } # _Dana Jacobsen_, May 10 2015
%o A181671 # To control memory use at cost of speed:
%o A181671 (Perl) use ntheory ":all"; my($n,$inc,$start,$sum)=(1e10,1e9,0,0); while ($start < $n) { $sum += scalar(@{ramanujan_primes($start,$start+$inc-1)}); $start += $inc; } say $sum; # _Dana Jacobsen_, May 10 2015
%o A181671 (Perl) use ntheory ":all"; say ramanujan_prime_count(10**$_) for 1..11; # _Dana Jacobsen_, Jan 03 2016
%Y A181671 Cf. A104272 (Ramanujan primes).
%Y A181671 Cf. A190502 (Number of Ramanujan primes <= 2^n).
%K A181671 nonn,more
%O A181671 1,2
%A A181671 _T. D. Noe_, Nov 18 2010
%E A181671 a(10)-a(11) from _Dana Jacobsen_, Dec 29 2014
%E A181671 a(12) from _Dana Jacobsen_, Sep 08 2015
%E A181671 a(13)-a(14) from _Dana Jacobsen_, Jan 03 2016
%E A181671 a(15)-a(17) from _Dana Jacobsen_, Apr 26 2017