

A179196


Number of primes up to the nth Ramanujan prime: A000720(A104272(n)).


11



1, 5, 7, 10, 13, 15, 17, 19, 20, 25, 26, 28, 31, 35, 36, 39, 41, 42, 49, 50, 51, 52, 53, 56, 57, 60, 63, 64, 69, 70, 73, 74, 79, 80, 81, 83, 84, 85, 89, 93, 94, 96, 104, 105, 107, 108, 109, 110, 111, 116, 117, 118, 119, 120, 123, 128, 129, 131, 133, 136, 140, 142, 143
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OFFSET

1,2


COMMENTS

a(n) = k = pi(p_k) = pi(R_n) That is, p_k is the nth Ramanujan prime, R_n the kth prime. pi(R_n) where pi is the prime number counting function and R_n is the nth Ramanujan prime.


REFERENCES

H. W. Shapiro, Iterates of arithmetic functions and a property of the sequence of primes, Pacific J. Math. Volume 3, Number 3 (1953), 647655.
J. Sondow, Ramanujan Primes and Bertrand's Postulate, American Mathematical Monthly, Volume 116, Number 7, AugustSeptember 2009 , pp. 630635(6)


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
S. Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc., 11 (1919), 181182.
J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly 116 (2009) 630635.
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
Wikipedia, Ramanujan prime


FORMULA

a(n) = rho(n) in the paper by Sondow, Nicholson, and Noe.
prime(a(n)) = R_n = A104272(n).


EXAMPLE

The 10th Ramanujan Prime is 97. Pi(97) = 25. So, a(10) = 25.


CROSSREFS

Cf. A168421, A168425.
Sequence in context: A154689 A175766 A243187 * A024325 A060873 A186542
Adjacent sequences: A179193 A179194 A179195 * A179197 A179198 A179199


KEYWORD

nonn


AUTHOR

John W. Nicholson, Jul 02 2010


STATUS

approved



