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 A177407 Form triangle of weighted Farey fractions; read denominators by rows. 6
 1, 1, 1, 3, 3, 1, 1, 5, 7, 3, 9, 9, 3, 7, 5, 1, 1, 7, 11, 5, 17, 19, 7, 17, 13, 3, 5, 7, 9, 27, 27, 9, 7, 5, 3, 13, 17, 7, 19, 17, 5, 11, 7, 1, 1, 9, 15, 7, 25, 29, 11, 27, 21, 5, 9, 13, 17, 53, 55, 19, 15, 11, 7, 31, 41, 17, 47, 43, 13, 29, 19, 3, 11, 13, 5, 17, 19, 7, 23, 25, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Start with the list of fractions 0/1, 1/1 and repeatedly insert the weighted mediants (2a+c)/(2b+d) and (a+2c)/(b+2d) between every pair of adjacent elements a/b and c/d of the list. The fractions are to be reduced before the insertion step. REFERENCES James Propp, Posting to the Math Fun Mailing List, Dec 10 2010. LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..29533 (first 10 rows of triangle) Dhroova Aiylam, Tanya Khovanova, Weighted Mediants and Fractals, arXiv:1711.01475 [math.NT], 2017. EXAMPLE Triangle begins: 0 1 - - 1 1 0 1 2 1 - - - - 1 3 3 1 0 1 2 1 4 5 2 5 4 1 - - - - - - - - - - 1 5 7 3 9 9 3 7 5 1 CROSSREFS Cf. A177405, A177903, A006842/A006843. Sequence in context: A220837 A187371 A056611 * A135669 A132729 A196493 Adjacent sequences:  A177404 A177405 A177406 * A177408 A177409 A177410 KEYWORD nonn,frac,tabl,easy AUTHOR N. J. A. Sloane, Dec 10 2010 EXTENSIONS a(44)-a(80) and some corrected terms from Nathaniel Johnston, Apr 12 2011 STATUS approved

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Last modified May 17 19:39 EDT 2021. Contains 343988 sequences. (Running on oeis4.)