A177804 Least Ramanujan prime beginning a run of n Ramanujan primes associated with a sharp prime gap.

11, 4919, 1439, 7187, 37547, 210143, 3376943, 663563, 4429739, 17939627, 12034427, 47901143, 12870359, 136839779, 37904807, 26304659, 51917927, 1723126247, 181914119, 1031710259, 5864553599, 33299639987, 27219781703, 28176693947, 116010934619, 16052746559

Offset

1,1

Comments

Let the run of n Ramanujan primes begin with p and end with q. Then p is in this sequence if it is the least Ramanujan prime such that the range of numbers from (p+1)/2 to (q+1)/2 are composite and the two numbers bounding that range, (p-1)/2 and (q+3)/2, are prime.

Links

Table of n, a(n) for n = 1..26

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.

Example

1439, 1479, and 1451 is a run of three Ramanujan primes. The range (1439+1)/2 to (1451+1)/2 consists of the composite numbers 720 to 726. That range is bounded by the two primes 719 and 727.

Crossrefs

Cf. A104272 (Ramanujan primes).

Sequence in context: A024152 A265958 A147668 * A023334 A216790 A068730

Adjacent sequences: A177801 A177802 A177803 * A177805 A177806 A177807

Keyword

nonn

Author

T. D. Noe, Dec 12 2010 and May 03 2011

Extensions

a(12)-a(26) from Dana Jacobsen, Apr 29 2015

Status

approved