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

1,1

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

Gord Palameta, Table of n, a(n) for n = 1..47

Carlos Rivera, The prime puzzles & problems connection, number 74

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. A001348, A000668, A000043.

Subsequence of: A007953, A007605.

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

Sequence in context: A367712 A016619 A368069 * A352709 A216627 A355927

Adjacent sequences: A066535 A066536 A066537 * A066539 A066540 A066541

Keyword

base,nonn

Author

Robert G. Wilson v, Jan 06 2002

Extensions

Definition corrected by Omar E. Pol, Apr 01 2008

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

Status

approved