

A059305


Pi(Mersenne(n)): index of nth Mersenne prime.


14




OFFSET

1,1


COMMENTS

Similar to A016027, but gives the number of the nth Mersenne prime (rather than the number of the prime exponent).
A subsequence of A007053 and A086690.


LINKS

Table of n, a(n) for n=1..9.
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), 235245.
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^e1; h = Mod(2, n); for (k=1, e2, h=2*h*h1); return(0==h) \\ after Joerg Arndt in A000043
forprime(p=1, , if(LL(p), print1(primepi(2^p1), ", "))) \\ 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



