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A177804 Least Ramanujan prime beginning a run of n Ramanujan primes associated with a sharp prime gap. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 12:05 EDT 2021. Contains 348168 sequences. (Running on oeis4.)