Geodesic
On continued fractions of equal length
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 96-99.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article gives a one-parameter family of rational numbers whose expansions in reduced regular continued fractions (Hirzebruch fractions) have equal lengths. 
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A. V. Ustinov. On continued fractions of equal length. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 1, pp. 96-99. http://geodesic.mathdoc.fr/item/DVMG_2014_14_1_a8/

[1] Grekhem R. L., Knut D. E., Patashnik O., Konkretnaya matematika. Osnovanie informatiki, Mir, M., 1998

[2] Math. Notes, 79:1 (2006), 146–147 | DOI | DOI | MR | Zbl

[3] Perron O., Die Lehre von den Kettenbruechen (Band 1)., B.G. Teubner Verlagsgesellschaft, Stuttgart, 1954 | MR | Zbl

[4] Zaimi G., Length of Hirzebruch continued fractions http://mathoverflow.net/