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Sum of terms in the continued logarithm expansion of n.
0

%I #12 Apr 05 2024 11:10:14

%S 0,1,2,2,4,3,4,3,6,5,6,4,4,5,7,4,8,7,8,6,6,7,9,5,7,5,10,6,10,8,11,5,

%T 10,9,10,8,8,9,11,7,9,7,12,8,12,10,13,6,11,8,10,6,10,11,9,7,11,11,12,

%U 9,14,12,16,6,12,11,12,10,10,11,13,9,11,9,14,10,14,12,15,8,13,10,12,8,12,13,11,9,13,13,14,11,16,14,18,7,16,12,14,9,12,11,11,7

%N Sum of terms in the continued logarithm expansion of n.

%H Jon Borwein, Neil Calkin, Scott Lindstrom, and Andrew Mattingly, <a href="https://carmamaths.org/resources/jon/clogs.pdf">Continued logarithms and associated continued fractions</a>, preprint, 2016.

%e For n = 7 the expansion is <2,0,1,1> which sums to 4.

%Y Cf. A273126, which gives the length of the expansion (as opposed to the sum of terms as counted here).

%K nonn

%O 1,3

%A _Jeffrey Shallit_, Jun 12 2016