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A179196 Number of primes up to the n-th 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = k = pi(p_k) = pi(R_n) That is, p_k is the n-th Ramanujan prime, R_n the k-th prime. pi(R_n) where pi is the prime number counting function and R_n is the n-th 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), 647-655.

J. Sondow, Ramanujan Primes and Bertrand's Postulate, American Mathematical Monthly, Volume 116, Number 7, August-September 2009 , pp. 630-635(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), 181-182.

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

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

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Last modified October 2 10:42 EDT 2014. Contains 247538 sequences.