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!)
A143577 Numbers k such that the continued fraction of (1 + sqrt(k))/2 has period 9. 3
73, 97, 233, 277, 349, 353, 613, 821, 877, 1073, 1181, 1189, 1277, 1285, 1313, 1385, 1613, 1637, 1693, 1745, 1865, 2357, 2581, 2777, 3233, 3557, 3989, 4157, 4469, 4517, 4553, 4709, 4889, 4925, 4933, 5245, 5261, 5305, 5597, 6113, 6205, 6253, 7213, 7585, 7837, 8885 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
For primes in this sequence see A146354.
Superset of A146354. - R. J. Mathar, Nov 05 2008
LINKS
EXAMPLE
a(1) = 73 because continued fraction of (1+sqrt(73))/2 = 4, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, ... has period (1, 3, 2, 1, 1, 2, 3, 1, 7) length 9 .
MAPLE
isA143577 := proc(k) local c; try c := numtheory[cfrac](1/2+sqrt(k)/2, 'periodic', 'quotients') ; if nops(c[2]) = 9 then RETURN(true) ; else RETURN(false) ; fi; catch: RETURN(false) ; end try; end: for k from 2 to 80000 do if isA143577(k) then printf("%d, ", k) ; fi; od: # R. J. Mathar, Nov 05 2008
MATHEMATICA
Select[Range[1000], !IntegerQ @ Sqrt[#] && Length[ContinuedFraction[(1 + Sqrt[#])/2][[2]]] == 9 &] (* Amiram Eldar, Mar 19 2020 *)
CROSSREFS
Sequence in context: A107008 A141375 A140621 * A146354 A050958 A139990
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 30 2008
EXTENSIONS
Extended by R. J. Mathar, Nov 05 2008
More terms from Amiram Eldar, Mar 19 2020
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 March 19 07:04 EDT 2024. Contains 370953 sequences. (Running on oeis4.)