A190502 Number of Ramanujan primes <= 2^n.

0, 1, 1, 1, 2, 4, 7, 13, 23, 42, 75, 137, 255, 463, 872, 1612, 3030, 5706, 10749, 20387, 38635, 73584, 140336, 268216, 513705, 985818, 1894120, 3645744, 7027290, 13561906, 26207278, 50697533, 98182656, 190335585, 369323301, 717267167, 1394192236, 2712103833

Offset

0,5

Links

Dana Jacobsen, Table of n, a(n) for n = 0..56

Prog

(PARI) \\ With RR[.] is a list of A104272(.). The output of this program is n, a(n), and RR[a(n)].
j=0; while(2^j<RR[10^8], {n=1; while(RR[n]<=2^j, n++); if(n<=1, print(j, " ", 0, " none"), print(j, " ", n-1, " ", RR[n-1])); j++}); \\ John W. Nicholson, Dec 01 2012
(Perl) use ntheory ":all"; sub a190502 { scalar(@{ramanujan_primes(1 << shift)}) } say a190502($_) for 0..20; # Dana Jacobsen, Dec 19 2015
(Perl) use ntheory ":all"; my $t = 0; for my $e (1..32) { $t += scalar(@{ramanujan_primes(2**($e-1)+1, 2**$e)}); say "$e $t" } # Dana Jacobsen, Dec 19 2015
(Perl) use ntheory ":all"; say ramanujan_prime_count(2**$_) for 0..47; # Dana Jacobsen, Jan 03 2016

Crossrefs

Cf. A007053, A036378, A104272, A181671, A190501.

Sequence in context: A165648 A287381 A078038 * A048888 A280027 A026724

Adjacent sequences: A190499 A190500 A190501 * A190503 A190504 A190505

Keyword

nonn

Author

John W. Nicholson, May 11 2011

Extensions

Extended by T. D. Noe, May 11 2011

Extended to n = 32 by John W. Nicholson, Dec 01 2012

a(33)-a(41) from Dana Jacobsen, Dec 19 2015

Status

approved