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

1,2

Links

Table of n, a(n) for n=1..17.

Mathematica

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]]]]}]

Prog

(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

Crossrefs

Cf. A104272 (Ramanujan primes).

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

Sequence in context: A037614 A138782 A155606 * A058111 A223120 A240275

Adjacent sequences: A181668 A181669 A181670 * A181672 A181673 A181674

Keyword

nonn,more

Author

T. D. Noe, Nov 18 2010

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

Status

approved