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Sum of the digits of the n-th Mersenne prime (A000668).
3

%I #36 Oct 16 2024 09:19:27

%S 3,7,4,10,19,13,28,46,73,112,139,154,697,847,1675,3106,3106,4258,5755,

%T 5950,13216,13693,14980,27202,28939,31339,60337,116455,149365,179488,

%U 291745,1026544,1163443,1704376,1893388,4038358,4092673,9440671,18243946,28445131,32580433,35170384,41201947,44142151,50349694,57766339,58416637

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

%C From _Gord Palameta_, Jul 21 2018: (Start)

%C 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.)

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

%H Amiram Eldar, <a href="/A066538/b066538.txt">Table of n, a(n) for n = 1..48</a> (terms 1..47 from Gord Palameta)

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_074.htm">Puzzle 74.- SOD(2^6972593-1)</a>, The Prime Puzzles & Problems Connection.

%F a(n) = A007953(A000668(n)). - _Amiram Eldar_, Oct 16 2024

%t ep = {the exponents from A000043}; a = {}; Do[ a = Append[a, Apply[ Plus, IntegerDigits[ 2^ep[[n]] - 1]]], {n, 1, 47} ]; a

%t (* Second program: *)

%t Array[Total@ IntegerDigits[2^MersennePrimeExponent@ # - 1] &, 45] (* _Michael De Vlieger_, Jul 22 2018 *)

%Y Cf. A000043, A000668, A007953, A001348.

%Y Subsequence of: A007953, A007605.

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

%K base,nonn

%O 1,1

%A _Robert G. Wilson v_, Jan 06 2002

%E Definition corrected by _Omar E. Pol_, Apr 01 2008

%E a(38)-a(47) from _Gord Palameta_, Jul 21 2018