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A216251 a(n) = n-th decimal digit of the decimal expansion of the n-th Farey fraction ordered by rank. 1
0, 9, 0, 3, 6, 0, 0, 0, 0, 0, 0, 6, 3, 4, 5, 5, 2, 5, 8, 0, 0, 0, 0, 1, 2, 4, 5, 7, 8, 0, 0, 0, 0, 0, 1, 7, 3, 5, 5, 3, 7, 1, 9, 3, 6, 3, 6, 0, 1, 3, 7, 6, 3, 1, 6, 9, 9, 1, 7, 5, 7, 5, 2, 7, 7, 6, 3, 6, 6, 3, 3, 6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 8, 7, 4, 9, 7, 1, 0, 5, 7, 1, 9, 1, 4, 5, 5, 9, 5, 7, 8, 1, 2, 4, 8, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Used as an example in the Schaffter link to support Cantor's diagonal argument. Most probably irrational and possible normal.
REFERENCES
Martin Aigner and Günter M. Ziegler, Proofs from THE BOOK, Second Edition, Springer-Verlag, Berlin Heidelberg NY, Section of Analysis, Chptr 15, "Sets, function, and the continuum hypothesis", 2000, pp. 87 - 98.
Georg Cantor, Über eine Eigenschaft des Inbegriffes aller reellen Zahlen ("On the Characteristic Property of All Real Numbers")
Timothy Gowers, Editor, with June Barrow-Green & Imre Leader, Assc. Editors, The Princeton Companion to Mathematics, Princeton Un. Press, Princeton & Oxford, 2008, pp. 171 & 779
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §7.5 Transfinite Numbers, pp. 257-262.
LINKS
Eric Weisstein's World of Mathematics, Cantor Diagonal Method
FORMULA
The n-th decimal digit of the n-th Farey fraction in order, i.e., 0, 1 (=0.99999..., 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5, 1/6, 5/6, 1/7, 2/7, ..., . (this is A038566/A038567)
EXAMPLE
The first decimal digit of 0 is 0, the second decimal digit of 1 (=0.99999...) is 9, the third decimal digit of 1/2 is 0, the fourth decimal digit of 1/3 is 3, the fifth decimal digit of 2/3 is 6, ..., the twelfth decimal digit of 1/6 is 6, the thirteenth decimal digit of 5/6 is 3, the fourteenth decimaldigit of 1/7 is 4, ..., .
MATHEMATICA
FareyOrder[n_] := Select[ Table[a/n, {a, n}], Denominator[#] == n &]; lst = Join[{0, .999999}, Flatten[ Table[ FareyOrder[n], {n, 2, 19}]]]; f[n_] := RealDigits[ lst[[n]], 10, 2 n][[1, n]]; Array[f, 105]
CROSSREFS
Sequence in context: A367961 A093961 A154903 * A011110 A211884 A154464
KEYWORD
easy,base,nonn
AUTHOR
Robert G. Wilson v, Mar 14 2013
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)