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A179196
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Number of primes up to the n-th Ramanujan prime: A000720(A104272(n)).
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12
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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
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1,2
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COMMENTS
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a(n) = k = pi(p_k) = pi(R_n), where pi is the prime number counting function and R_n is the n-th Ramanujan prime. I.e., p_k, the k-th prime, is the n-th Ramanujan prime.
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LINKS
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Christian Axler, On Ramanujan primes, Functiones et Approximatio Commentarii Mathematici (2019).
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FORMULA
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a(n) = rho(n) in the paper by Sondow, Nicholson, and Noe.
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EXAMPLE
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The 10th Ramanujan prime is 97, and pi(97) = 25, so a(10) = 25.
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MATHEMATICA
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f[n_] := With[{s = Table[{k, PrimePi[k] - PrimePi[k/2]}, {k, Prime[3 n]}]}, Table[1 + First@ Last@ Select[s, Last@ # == i - 1 &], {i, n}]]; PrimePi@ f@ 63 (* Michael De Vlieger, Nov 14 2017, after Jonathan Sondow at A104272 *)
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PROG
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(Perl) use ntheory ":all"; say prime_count(nth_ramanujan_prime($_)) for 1..100; # Dana Jacobsen, Dec 25 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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