

A028335


Number of digits in nth Mersenne prime.
(Formerly N0189)


9



1, 1, 2, 3, 4, 6, 6, 10, 19, 27, 33, 39, 157, 183, 386, 664, 687, 969, 1281, 1332, 2917, 2993, 3376, 6002, 6533, 6987, 13395, 25962, 33265, 39751, 65050, 227832, 258716, 378632, 420921, 895932, 909526, 2098960, 4053946, 6320430, 7235733, 7816230, 9152052, 9808358, 11185272
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OFFSET

1,3


COMMENTS

Apply p>floor(p*log(2)/log(10))+1 to A000043.


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 19.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).


LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..47
C. K. Caldwell, Mersenne Primes
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012.


FORMULA

a(n) = A055642(A000668(n)).  Michel Marcus, Apr 07 2018


MAPLE

seq(length(numtheory:mersenne([i])), i=1..45); # Robert Israel, Feb 02 2018


MATHEMATICA

IntegerLength[2^Array[MersennePrimeExponent, 45]  1] (* JeanFrançois Alcover, Feb 17 2018 *)


CROSSREFS

See A000043, which is the main entry for this sequence. Cf. A000668, A055642.
Sequence in context: A243930 A064778 A317491 * A007464 A210733 A265564
Adjacent sequences: A028332 A028333 A028334 * A028336 A028337 A028338


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Enoch Haga, Dec 18 2001
One more term from Harry J. Smith, Apr 17 2003
4053946 from Omar E. Pol, Oct 28 2007
a(40)a(41) from Jason Kimberley, Jan 05 2012
a(42)a(45) from Patrick J. McNab, Feb 01 2018


STATUS

approved



