Farey sequence (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Farey sequence" in English language version.

refsWebsite

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11doi.org

2^nd place

5arxiv.org

69^th place

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3archive.org

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3semanticscholar.org

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2worldcat.org

5^th place

2web.archive.org

1^st place

2harvard.edu

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2digizeitschriften.de

5,626^th place

8,880^th place

2jstor.org

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2cern.ch

1,959^th place

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1books.google.com

3^rd place

1cut-the-knot.org

low place

1oeis.org

742^nd place

538^th place

1colgate.edu

low place

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1uwaterloo.ca

3,153^rd place

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1numdam.org

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1mdpi.com

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1ams.org

451^st place

277^th place

1maths.org

low place

ams.org

Austin, David (December 2008). "Trees, Teeth, and Time: The mathematics of clock making". American Mathematical Society. Rhode Island. Archived from the original on 4 February 2020. Retrieved 28 September 2020.

archive.org

Hardy, G.H.; Wright, E.M. (1979). An Introduction to the Theory of Numbers (Fifth ed.). Oxford University Press. Chapter III. ISBN 0-19-853171-0.
John Farey Sr. (1816), "On a curious property of vulgar fractions", Philosophical Magazine, 47: 385–386
Edwards, Harold M. (1974). "12.2 Miscellany. The Riemann Hypothesis and Farey Series". In Smith, Paul A.; Ellenberg, Samuel (eds.). Riemann's Zeta Function. Pure and Applied Mathematics. New York: Academic Press. pp. 263–267. ISBN 978-0-08-087373-2. OCLC 316553016. Retrieved 30 September 2020.

arxiv.org

Tomas Garcia, Rogelio (July 2024). "Farey Fractions with Equal Numerators and the Rank of Unit Fractions" (PDF). Integers. 24. arXiv:2404.08283. doi:10.5281/zenodo.12685697.
Martin, Greg (2009). "A product of Gamma function values at fractions with the same denominator". arXiv:0907.4384 [math.CA].
Wehmeier, Stefan (2009). "The LCM(1,2,...,n) as a product of sine values sampled over the points in Farey sequences". arXiv:0909.1838 [math.CA].
Zhenhua Li, A.; Harter, W.G. (2015). "Quantum Revivals of Morse Oscillators and Farey–Ford Geometry". Chem. Phys. Lett. 633: 208–213. arXiv:1308.4470. Bibcode:2015CPL...633..208L. doi:10.1016/j.cplett.2015.05.035. S2CID 66213897.
Tomas, Rogelio (2020). "Imperfections and corrections". arXiv:2006.10661 [physics.acc-ph].

books.google.com

Guthery, Scott B. (2011). "1. The Mediant". A Motif of Mathematics: History and Application of the Mediant and the Farey Sequence. Boston: Docent Press. p. 7. ISBN 978-1-4538-1057-6. OCLC 1031694495. Retrieved 28 September 2020.

cern.ch

rtomas.web.cern.ch

Tomas Garcia, Rogelio (August 2020). "Equalities between greatest common divisors involving three coprime pairs" (PDF). Notes on Number Theory and Discrete Mathematics. 26 (3): 5–7. doi:10.7546/nntdm.2020.26.3.5-7. S2CID 225280271.

cds.cern.ch

Tomas, R. (2014). "From Farey sequences to resonance diagrams" (PDF). Physical Review Special Topics - Accelerators and Beams. 17 (1): 014001. Bibcode:2014PhRvS..17a4001T. doi:10.1103/PhysRevSTAB.17.014001.

colgate.edu

math.colgate.edu

Tomas Garcia, Rogelio (July 2024). "Farey Fractions with Equal Numerators and the Rank of Unit Fractions" (PDF). Integers. 24. arXiv:2404.08283. doi:10.5281/zenodo.12685697.

cut-the-knot.org

Beiler, Albert H. (1964). Recreations in the Theory of Numbers (Second ed.). Dover. Chapter XVI. ISBN 0-486-21096-0. Cited in "Farey Series, A Story". Cut-the-Knot.

digizeitschriften.de

Franel, Jérôme (1924). "Les suites de Farey et le problème des nombres premiers". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse (in French): 198–201.
Landau, Edmund (1924). "Bemerkungen zu der vorstehenden Abhandlung von Herrn Franel". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse (in German): 202–206.

doi.org

Tomas Garcia, Rogelio (July 2024). "Farey Fractions with Equal Numerators and the Rank of Unit Fractions" (PDF). Integers. 24. arXiv:2404.08283. doi:10.5281/zenodo.12685697.
Tomas Garcia, Rogelio (2025). "New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy". Mathematics. 13 (1): 140. doi:10.3390/math13010140.
Tomas Garcia, Rogelio (August 2020). "Equalities between greatest common divisors involving three coprime pairs" (PDF). Notes on Number Theory and Discrete Mathematics. 26 (3): 5–7. doi:10.7546/nntdm.2020.26.3.5-7. S2CID 225280271.
Eliahou, Shalom (August 1993). "The 3x+1 problem: new lower bounds on nontrivial cycle lengths". Discrete Mathematics. 118 (1–3): 45–56. doi:10.1016/0012-365X(93)90052-U.
Zhenhua Li, A.; Harter, W.G. (2015). "Quantum Revivals of Morse Oscillators and Farey–Ford Geometry". Chem. Phys. Lett. 633: 208–213. arXiv:1308.4470. Bibcode:2015CPL...633..208L. doi:10.1016/j.cplett.2015.05.035. S2CID 66213897.
Tomas, R. (2014). "From Farey sequences to resonance diagrams" (PDF). Physical Review Special Topics - Accelerators and Beams. 17 (1): 014001. Bibcode:2014PhRvS..17a4001T. doi:10.1103/PhysRevSTAB.17.014001.
Harabor, Daniel Damir; Grastien, Alban; Öz, Dindar; Aksakalli, Vural (26 May 2016). "Optimal Any-Angle Pathfinding In Practice". Journal of Artificial Intelligence Research. 56: 89–118. doi:10.1613/jair.5007.
Hew, Patrick Chisan (19 August 2017). "The Length of Shortest Vertex Paths in Binary Occupancy Grids Compared to Shortest r-Constrained Ones". Journal of Artificial Intelligence Research. 59: 543–563. doi:10.1613/jair.5442.
Blake, Jean A. (1966). "Some Characteristic Properties of the Farey Series". The American Mathematical Monthly. 73 (1): 50–52. doi:10.2307/2313922. JSTOR 2313922.
Kurt Girstmair; Girstmair, Kurt (2010). "Farey Sums and Dedekind Sums". The American Mathematical Monthly. 117 (1): 72–78. doi:10.4169/000298910X475005. JSTOR 10.4169/000298910X475005. S2CID 31933470.
Hall, R. R.; Shiu, P. (2003). "The Index of a Farey Sequence". Michigan Math. J. 51 (1): 209–223. doi:10.1307/mmj/1049832901.

harvard.edu

ui.adsabs.harvard.edu

Zhenhua Li, A.; Harter, W.G. (2015). "Quantum Revivals of Morse Oscillators and Farey–Ford Geometry". Chem. Phys. Lett. 633: 208–213. arXiv:1308.4470. Bibcode:2015CPL...633..208L. doi:10.1016/j.cplett.2015.05.035. S2CID 66213897.
Tomas, R. (2014). "From Farey sequences to resonance diagrams" (PDF). Physical Review Special Topics - Accelerators and Beams. 17 (1): 014001. Bibcode:2014PhRvS..17a4001T. doi:10.1103/PhysRevSTAB.17.014001.

jstor.org

Blake, Jean A. (1966). "Some Characteristic Properties of the Farey Series". The American Mathematical Monthly. 73 (1): 50–52. doi:10.2307/2313922. JSTOR 2313922.
Kurt Girstmair; Girstmair, Kurt (2010). "Farey Sums and Dedekind Sums". The American Mathematical Monthly. 117 (1): 72–78. doi:10.4169/000298910X475005. JSTOR 10.4169/000298910X475005. S2CID 31933470.

maths.org

nrich.maths.org

"Farey Approximation". NRICH.maths.org. Archived from the original on 19 November 2018. Retrieved 18 November 2018.

mdpi.com

Tomas Garcia, Rogelio (2025). "New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy". Mathematics. 13 (1): 140. doi:10.3390/math13010140.

numdam.org

archive.numdam.org

Dress, F. (1999). "Discrépance des suites de Farey" (PDF). J. Théorie des Nr. Bordx. 11.

oeis.org

Sloane, N. J. A. (ed.). "Sequence A005728". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

semanticscholar.org

api.semanticscholar.org

Tomas Garcia, Rogelio (August 2020). "Equalities between greatest common divisors involving three coprime pairs" (PDF). Notes on Number Theory and Discrete Mathematics. 26 (3): 5–7. doi:10.7546/nntdm.2020.26.3.5-7. S2CID 225280271.
Zhenhua Li, A.; Harter, W.G. (2015). "Quantum Revivals of Morse Oscillators and Farey–Ford Geometry". Chem. Phys. Lett. 633: 208–213. arXiv:1308.4470. Bibcode:2015CPL...633..208L. doi:10.1016/j.cplett.2015.05.035. S2CID 66213897.
Kurt Girstmair; Girstmair, Kurt (2010). "Farey Sums and Dedekind Sums". The American Mathematical Monthly. 117 (1): 72–78. doi:10.4169/000298910X475005. JSTOR 10.4169/000298910X475005. S2CID 31933470.

uwaterloo.ca

cs.uwaterloo.ca

Tomas, Rogelio (January 2022). "Partial Franel sums" (PDF). Journal of Integer Sequences. 25 (1).

web.archive.org

Austin, David (December 2008). "Trees, Teeth, and Time: The mathematics of clock making". American Mathematical Society. Rhode Island. Archived from the original on 4 February 2020. Retrieved 28 September 2020.
"Farey Approximation". NRICH.maths.org. Archived from the original on 19 November 2018. Retrieved 18 November 2018.

worldcat.org

search.worldcat.org

Guthery, Scott B. (2011). "1. The Mediant". A Motif of Mathematics: History and Application of the Mediant and the Farey Sequence. Boston: Docent Press. p. 7. ISBN 978-1-4538-1057-6. OCLC 1031694495. Retrieved 28 September 2020.
Edwards, Harold M. (1974). "12.2 Miscellany. The Riemann Hypothesis and Farey Series". In Smith, Paul A.; Ellenberg, Samuel (eds.). Riemann's Zeta Function. Pure and Applied Mathematics. New York: Academic Press. pp. 263–267. ISBN 978-0-08-087373-2. OCLC 316553016. Retrieved 30 September 2020.