A174641 Smallest prime that begins a run of n consecutive primes that are not Ramanujan primes.

3, 3, 3, 73, 191, 191, 509, 2539, 2539, 5279, 9901, 9901, 9901, 11593, 11593, 55343, 55343, 55343, 55343, 55343, 174929, 174929, 174929, 225977, 225977, 225977, 225977, 225977, 534889, 534889, 534889, 534889, 534889, 534889, 534889, 534889, 2492317, 2492317

Offset: 1

Author

T. D. Noe, Nov 29 2010

Keywords

• nonn

Comments

The run of 10 consecutive non-Ramanujan primes was mentioned by Sondow.

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..107 (first 67 terms from T. D. Noe)
• J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010.
• 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, arXiv:1105.2249 [math.NT], 2011.
• 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. A104272 (Ramanujan primes), A174635 (non-Ramanujan primes).

Cf. A174602 (runs of Ramanujan primes).

Cf. A202187, A202188.

Programs

Mathematica

nn=10000; t=Table[0, {nn}]; len=Prime[3*nn]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s
				

Perl

use ntheory ":all";
my($k, $max, $start, $end, $inc, $p, $q, $r, $pi)
   = (0, 0, 0, 10, 1e9, 0, 2, [], prime_iterator(3));
while (1) {
  if (!@$r) {
    ($start, $end) = ($end+1, $end+$inc);
    $r = ramanujan_primes($start, $end);
  }
  ($p, $q, $k) = ($q, shift(@$r), 0);
  # $k = prime_count($p+1,$q-1);
  $k++ while $pi->() < $q;
  say ++$max," ",next_prime($p)   while $k > $max;
}
# Dana Jacobsen, Jul 14 2016