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A059305
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Pi(Mersenne(n)): index of n-th Mersenne prime.
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17
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OFFSET
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1,1
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COMMENTS
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Similar to A016027, but gives the number of the n-th Mersenne prime (rather than the number of the prime exponent).
A subsequence of A007053 and A086690.
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LINKS
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Table of n, a(n) for n=1..10.
Andrew R. Booker, The Nth Prime Page
C. K. Caldwell, Mersenne Primes
M. Deleglise and J. Rivat, Computing pi(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp., 65 (1996), 235-245.
Xavier Gourdon and Pascal Sebah, Counting primes
Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)
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FORMULA
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a(n) = A000720(A000668(n))
a(n) = A007053(A000043(n))
A000668(n) = A000040(a(n)). - Omar E. Pol, Jun 29 2012
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EXAMPLE
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Element 2 = 4 because Mersenne2 = (2^3)-1 = 7; 7 is the 4th prime.
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MATHEMATICA
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Array[PrimePi[2^MersennePrimeExponent[#] - 1] &, 8] (* Michael De Vlieger, Apr 21 2019 *)
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PROG
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(PARI) LL(e) = if(e==2, return(1)); my(n, h); n = 2^e-1; h = Mod(2, n); for (k=1, e-2, h=2*h*h-1); return(0==h) \\ after Joerg Arndt in A000043
forprime(p=1, , if(LL(p), print1(primepi(2^p-1), ", "))) \\ Felix Fröhlich, Apr 19 2019
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CROSSREFS
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Cf. A000043 Mersenne exponents, A000668 Mersenne primes, A016027 Pi(mersenne exponents), A001348 Mersenne numbers.
Sequence in context: A123421 A123430 A086690 * A191586 A120848 A320567
Adjacent sequences: A059302 A059303 A059304 * A059306 A059307 A059308
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KEYWORD
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nonn,hard,more
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AUTHOR
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Reto Keiser (rkeiser(AT)ee.ethz.ch), Jan 25 2001
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EXTENSIONS
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Revised by Max Alekseyev, Jul 20 2007
a(10) from David Baugh, Oct 08 2020
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STATUS
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approved
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