A174602 Smallest prime that begins a run of n Ramanujan primes that are consecutive primes.

2, 67, 227, 227, 227, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 2657, 562871, 793487, 809707, 809707, 984241, 984241, 984241, 6234619, 11652013, 41662651, 41662651, 41662651, 94653397, 383825567, 869730887, 953913871, 953913871, 953913871

Offset: 1

Author

T. D. Noe, Nov 29 2010

Keywords

• nonn

Comments

The first run of 13 consecutive Ramanujan primes was mentioned by Sondow.

Starting at index m = A191228(a(n)) in A190874(m), the first instance of a count of n - 1 consecutive 1's is seen. - John W. Nicholson, Dec 15 2011

Examples

			67 and 71 are the first two Ramanujan primes that are consecutive primes, so a(2) = 67.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..42
• 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), A174641 (runs of non-Ramanujan primes).

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 $r=ramanujan_primes(1e8); my $max = 0; for (0..$#$r-2) { my $k=0; $k++ while next_prime($r->[$+$k]) == $r->[$+$k+1]; say ++$max," ",$r->[$] while $k >= $max; } # _Dana Jacobsen, Jul 14 2016