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A174641 Smallest prime that begins a run of n consecutive primes that are not Ramanujan primes. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

T. D. Noe and Dana Jacobsen, Table of n, a(n) for n = 1..107 (first 67 terms from 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.

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<nn, t[[s+1]]=k], {k, len}]; t=t+1; t=Complement[Prime[Range[PrimePi[t[[-1]]]]], t]; ind=PrimePi[t]; d=Differences[ind]; cnt=0; n=1; Join[{2}, Reap[Do[If[d[[i]]==1, cnt++; If[cnt==n, Sow[t[[i-n+1]]]; n++], cnt=0], {i, Length[d]}]][[2, 1]]]

PROG

(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

CROSSREFS

Cf. A104272 (Ramanujan primes), A174635 (non-Ramanujan primes).

Cf. A174602 (runs of Ramanujan primes).

Cf. A202187, A202188.

Sequence in context: A174538 A340821 A091323 * A217671 A118539 A015665

Adjacent sequences:  A174638 A174639 A174640 * A174642 A174643 A174644

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 29 2010

STATUS

approved

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Last modified December 2 00:55 EST 2021. Contains 349435 sequences. (Running on oeis4.)