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Consider the Farey tree A049455/A049456; a(n) = row at which the denominator n first appears (assumes first row is labeled row 0).
2

%I #24 Dec 06 2024 11:21:54

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

%T 8,8,8,9,8,8,8,9,8,8,8,8,8,9,8,8,9,9,9,10,8,9,9,9,9,9,9,9,9,9,9,9,9,9,

%U 9,9,9,10,9,9,9,9,10,10,9,9,9,10,10,10,10,10,10,10,9,11,10,10,10,10,10,11

%N Consider the Farey tree A049455/A049456; a(n) = row at which the denominator n first appears (assumes first row is labeled row 0).

%C Equals A178031 - 1. See that entry for further information.

%H Richard J. Mathar, <a href="/A294443/a294443.pdf">The Kepler binary tree of reduced fractions</a>, 2017.

%Y Cf. A295783 (frequencies of this).

%K nonn,changed

%O 1,3

%A _N. J. A. Sloane_, Dec 16 2010