The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244658 a(n) = x/(x1-floor(x1)) where x = sqrt(n) - floor(sqrt(n)), x1 = 1/x, a(n) = -1 if division by zero, a(n) = 0 for nonintegers. 2
-1, 1, 2, -1, 1, 2, 0, 4, -1, 1, 2, 3, 0, 0, 6, -1, 1, 2, 0, 4, 0, 0, 0, 8, -1, 1, 2, 0, 0, 5, 0, 0, 0, 0, 10, -1, 1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12, -1, 1, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 14, -1, 1, 2, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, -1, 1, 2, 3, 0, 0, 6, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 18, -1, 1, 2, 0, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Inspired by the square root of three poem in "Harold and Kumar" the movie. This operation can be done in iterations for which some n seem to give all integer results after iteration k >= 2. Some of them have periodic properties similar to that of the continued fraction method (but not exactly the same). When a(n) is arranged as a table read by rows, the row sums would be A062731. See illustrations in links.
LINKS
Eric Weisstein's World of Mathematics, Periodic Continued Fraction
EXAMPLE
For n = 3, x = sqrt(3) - floor(sqrt(3)) = 0.732050807..., x1 = 1/x = 1/0.732050807... = 1.366025403..., x1 - floor(x1) = 0.366025403..., a(3) = 0.732050807.../0.366025402... = 2.
PROG
(Small Basic)
For n=1 To 500
x=math.Power(n, .5)
y=x-math.Floor(x)
If y<>0 Then
x1=1/y
x2=1/(x1-math.Floor(x1))
a1=x2/x1
a2=a1-math.floor(a1)
If a2 > 0.999999 or a2 < 0.0000001 then
a=math.Round(a1)
TextWindow.Write(a+", ")
Else
TextWindow.Write(0+", ")'noninteger
Endif
Else
TextWindow.Write(-1+", ")'zero division, Square number
EndIf
EndFor
CROSSREFS
Cf. A062731.
Sequence in context: A088226 A344309 A358338 * A117586 A307988 A268917
KEYWORD
sign
AUTHOR
Kival Ngaokrajang, Jul 04 2014
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 09:03 EDT 2024. Contains 373383 sequences. (Running on oeis4.)