A028335 Number of decimal digits in n-th Mersenne prime. (Formerly N0189)

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

Offset

1,3

References

Albert 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

Amiram Eldar, Table of n, a(n) for n = 1..48 (terms 1..47 from Ivan Panchenko)

Chris K. Caldwell, Mersenne Primes.

GIMPS, List of Known Mersenne Prime Numbers.

Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023.

Formula

a(n) = floor(A000043(n)*log(2)/log(10)) + 1.

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

Example

A000668(6) = 2^17-1 = 131071 has 6 decimal digits, so a(6) = 6.
A000668(10) = 2^89-1 = 618,970,019,642,690,137,449,562,111 has 27 digits, so a(10) = 27.

Maple

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

Mathematica

IntegerLength[2^Array[MersennePrimeExponent, 45] - 1] (* Jean-François Alcover, Feb 17 2018 *)
a[n_] := Floor[MersennePrimeExponent[n]/Log2[10]] + 1; Array[a, 48] (* Amiram Eldar, Oct 16 2024 *)

Crossrefs

See A000043, which is the main entry for this sequence.

Cf. A000668, A055642.

Sequence in context: A317491 A332295 A332576 * A346117 A007464 A210733

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

a(38) from Harry J. Smith, Apr 17 2003

a(39) 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