On Some Special Property of The Farey Sequence
In this paper, some special property of the Farey sequence is discussed. We prove in each term of the Farey sequence, the sum of elements in the denominator is two times of the sum of elements in the numerator. We also prove that the Farey sequence contains a palindrome structure.
Ainsworth, J., Dawson, M., Pianta, J. and Warwick, J.(2012). “The farey sequence,” https://www.maths.ed.ac.uk/v1ranick/fareyproject.pdf.
Burton, D. M. (1980). Elementary Number Theory, Allyn and Bacon, Inc., pp.150.
Cobeli, C. and Zaharescu, A. (2003). “The Haros-Farey sequence at two hundred years,”Acta Univ. Apulensis Math. Inform, 5, 1–38.
Hatcher, A. Topology of numbers, Chapter 1, http://www.math.cornell.ed/hatcher .
Hardy, G. H. and Wright, E. M. (1979). An Introduction to the Theory of Numbers, The Clarendon Press, Oxford University Press, New York, Fifth edition.
Kanemitsu, S. and Yoshimoto, M. (1996). Farey series and the Riemann hypothesis, Acta Arith., 75. 4, 351–374.
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