A234298 Ramanujan prime R_k such that pi(R_(k+1)) - pi(R_k) are record values: record Ramanujan prime A190874(k).

2, 71, 181, 503, 2531, 5273, 9887, 11587, 55339, 174917, 225961, 534883, 2492311, 5409337, 130449773, 141833603, 212583797, 658046911, 1183597123, 2897211971, 5602581277, 46992178547, 70637059291, 158465541049, 182591976709, 339683208863

Offset: 1

Author

John W. Nicholson, Dec 22 2013

Keywords

• nonn

Comments

These are the primes preceding the unique values of A174641. That sequence is the start of a run of non-Ramanujan primes, so the previous prime is the Ramanujan prime. - Dana Jacobsen, Jul 14 2016

Crossrefs

Record values are in A202186, index of A190874 at record terms in A202187, A202188 is the index of A168425 when A174641(n) = A168425(m); A202188(n) = m. A202187 is also the index of a(n).

Programs

Perl

perl -Mntheory=:all -nE 'my $n = $1 if /(\d+)$/; say ++$x," ",prev_prime($n) unless $seen{$n}++;' b174641.txt  # Dana Jacobsen, Jul 14 2016

Perl

use ntheory ":all"; my($max,$r)=(0,ramanujan_primes(1e7)); for (0..$#$r-1) { my $d=prime_count($r->[$+1])-prime_count($r->[$]); if ($d > $max) { say $r->[$]; $max=$d; } } # _Dana Jacobsen, Jul 14 2016

Extensions

a(20) to a(26) from Dana Jacobsen, Jul 14 2016