A181678 Number of twin Ramanujan prime pairs less than 10^n.

0, 0, 10, 73, 508, 3468, 25629, 194614, 1537504, 12447679, 102834428

Offset: 1

Author

T. D. Noe, Nov 18 2010

Keywords

• nonn
• more

Links

• J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly 116 (2009) 630-635.
• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2

Crossrefs

Cf. A178127 (lesser of twin Ramanujan primes), A007508 (number of twin primes pairs < 10^n), A190654 (twin Ramanujan primes).

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 $n (0..9) { my $r = ramanujan_primes(10**$n); my $t=0; for (0..$#$r-1) { $t++ if $r->[$+1] - $r->[$] == 2; } say "$n $t"; } # Dana Jacobsen, Sep 06 2015

Extensions

a(10)-a(11) from Dana Jacobsen, Apr 29 2015