OFFSET
1,1
COMMENTS
Theorem. If the sequence is unbounded, then there exist arbitrarily long sequences of consecutive primes p_k, p_(k+1),...,p_m such that every interval (p_i/2, p_(i+1)/2), i=k,k+1,...,m-1, contains a prime.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012) Article 12.5.4.
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.
PROG
(Haskell)
import Data.List (group)
a182426 n = a182426_list !! (n-1)
a182426_list = concatMap f $ group $ zipWith (-) (tail ips) ips where
f xs | head xs == 1 = reverse $ enumFromTo 2 $ length xs + 1
| otherwise = take (length xs) $ repeat 1
ips = map a049084 a166251_list
-- Reinhard Zumkeller, May 18 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 28 2012
EXTENSIONS
Data corrected: a(49)=2.
STATUS
approved