A066538 Sum of the digits of the n-th Mersenne prime (A000668).

3, 7, 4, 10, 19, 13, 28, 46, 73, 112, 139, 154, 697, 847, 1675, 3106, 3106, 4258, 5755, 5950, 13216, 13693, 14980, 27202, 28939, 31339, 60337, 116455, 149365, 179488, 291745, 1026544, 1163443, 1704376, 1893388, 4038358, 4092673, 9440671, 18243946, 28445131, 32580433, 35170384, 41201947, 44142151, 50349694, 57766339, 58416637

Offset: 1

Author

Robert G. Wilson v, Jan 06 2002

Keywords

• base
• nonn

Comments

From Gord Palameta, Jul 21 2018: (Start)

a(38) and a(39) were calculated by Enoch Haga, Sep 07 1999 and Dec 17 2001; a(40) through a(42) were calculated by Andrew Rupinski, Mar 12 2005. (See the Carlos Rivera link.)

It appears that asymptotically a(n)/A000043(n) = 9*log_10(2)/2. (End)

Links

• Amiram Eldar, Table of n, a(n) for n = 1..48 (terms 1..47 from Gord Palameta)
• Carlos Rivera, Puzzle 74.- SOD(2^6972593-1), The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A000043, A000668, A007953, A001348.

Subsequence of: A007953, A007605.

Cf. A001370 (sum of digits of 2^n).

Programs

Mathematica

ep = {the exponents from A000043}; a = {}; Do[ a = Append[a, Apply[ Plus, IntegerDigits[ 2^ep[[n]] - 1]]], {n, 1, 47} ]; a
(* Second program: *)
Array[Total@ IntegerDigits[2^MersennePrimeExponent@ # - 1] &, 45] (* Michael De Vlieger, Jul 22 2018 *)

Formula

a(n) = A007953(A000668(n)). - Amiram Eldar, Oct 16 2024

Extensions

Definition corrected by Omar E. Pol, Apr 01 2008

a(38)-a(47) from Gord Palameta, Jul 21 2018