login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006842 Numerators of Farey series of orders 1, 2, ....
(Formerly M0041)
17
0, 1, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 3, 1, 0, 1, 1, 1, 2, 1, 3, 2, 3, 4, 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 4, 5, 1, 0, 1, 1, 1, 1, 2, 1, 2, 3, 1, 4, 3, 2, 5, 3, 4, 5, 6, 1, 0, 1, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 5, 6, 7, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 4, 1, 5, 4, 3, 5, 2, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Row n has A005728(n) terms. - Michel Marcus, Jun 27 2014

REFERENCES

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 152

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 23.

W. J. LeVeque, Topics in Number Theory. Addison-Wesley, Reading, MA, 2 vols., 1956, Vol. 1, p. 154.

I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers. 2nd ed., Wiley, NY, 1966, p. 141.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10563

Andrey O. Matveev, Neighboring Fractions in Farey Subsequences, arXiv:0801.1981, 2008

N. J. A. Sloane, Stern-Brocot or Farey Tree

Eric Weisstein's World of Mathematics, Farey Sequence.

Index entries for sequences related to Stern's sequences

EXAMPLE

0/1, 1/1;

0/1, 1/2, 1/1;

0/1, 1/3, 1/2, 2/3, 1/1;

0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1;

0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1;

... = A006842/A006843

MAPLE

Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end: seq(numer(Farey(i)), i=1..5); # [Peter Luschny, Apr 28 2009]

MATHEMATICA

Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Flatten[ Table[ Numerator[ Farey[n]], {n, 0, 9}]] (* Robert G. Wilson v, Apr 08 2004 *)

PROG

(PARI) row(n) = {vf = [0]; for (k=1, n, for (m=1, k, vf = concat(vf, m/k); ); ); vf = vecsort(Set(vf)); for (i=1, #vf, print1(numerator(vf[i]), ", ")); } \\ Michel Marcus, Jun 27 2014

CROSSREFS

Cf. A006843, A049455, A049456, A007305, A007306. Also A177405/A177407.

Sequence in context: A205217 A054635 A003137 * A219967 A060505 A211452

Adjacent sequences:  A006839 A006840 A006841 * A006843 A006844 A006845

KEYWORD

nonn,nice,frac,tabf

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Robert G. Wilson v, Apr 08 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified October 25 22:07 EDT 2014. Contains 248558 sequences.