A066538 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

FORMULA

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

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 *)

CROSSREFS

Cf. A000043, A000668, A007953, A001348.