

A192820


2Ramanujan primes: the interval (x/2,x] has at least n Ramanujan primes for x >= a(n) but not for x = a(n)  1.


8



11, 41, 59, 97, 149, 151, 227, 229, 233, 239, 263, 307, 367, 373, 401, 409, 569, 571, 587, 593, 599, 641, 643, 647, 653, 719, 751, 821, 937, 941, 1009, 1019, 1021, 1031, 1049, 1051, 1061, 1063, 1217, 1367, 1373, 1423, 1427, 1439, 1481, 1487, 1549, 1553, 1559
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OFFSET

1,1


COMMENTS

It is conjectured that primepi(a(n)) <= 7*n for all n.  T. D. Noe, Aug 26 2011
Paksoy (2012) denotes a(n) by R'_n and calls it "the nth derived Ramanujan prime." He proves the bounds on R'_n below.  Jonathan Sondow, Oct 29 2012


LINKS



FORMULA

R(2n) <= a(n) < R(3n), where R(n) = the nth Ramanujan prime (Paksoy 2012).
p(4n) < a(n) < p(9n), where p(n) = the nth prime (Paksoy 2012).
a(n) < p(8n) for n >= 5315 (Paksoy 2012).
R(2n) ~ a(n) ~ p(4n) as n > oo (Paksoy 2012).


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



