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 A059305 Pi(Mersenne(n)): index of n-th Mersenne prime. 14
 2, 4, 11, 31, 1028, 12251, 43390, 105097565, 55890484045084135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS 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) FORMULA a(n) = A000720(A000668(n)) a(n) = A007053(A000043(n)) A000668(n) = A000040(a(n)). - Omar E. Pol, Jun 29 2012 EXAMPLE Element 2 = 4 because Mersenne2 = (2^3)-1 = 7; 7 is the 4th prime. MATHEMATICA Array[PrimePi[2^MersennePrimeExponent[#] - 1] &, 8] (* Michael De Vlieger, Apr 21 2019 *) PROG (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 CROSSREFS 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 KEYWORD nonn,hard,more AUTHOR Reto Keiser (rkeiser(AT)ee.ethz.ch), Jan 25 2001 EXTENSIONS Revised by Max Alekseyev, Jul 20 2007 STATUS approved

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Last modified December 10 12:30 EST 2019. Contains 329895 sequences. (Running on oeis4.)