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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A233592 Natural numbers n such that the continued fraction expansion sqrt(n) = c(1)+c(1)/(c(2)+c(2)/(c(3)+c(3)/....)) is periodic. 3
2, 3, 5, 6, 8, 10, 11, 12, 15, 17, 18, 20, 24, 26, 27, 30, 35, 37, 38, 39, 40, 42, 44, 45, 48, 50, 51, 56, 63, 65, 66, 68, 72, 80, 82, 83, 84, 87, 90, 99, 101, 102, 104, 105, 108, 110, 120, 122, 123, 132, 143, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For more details on this type of expansions, see A233582.

The cases with aperiodic expansions are listed in A233593.

All the listed cases become periodic after just two leading terms (it is a conjecture that this behavior is general); the validity of their expansions was explicitly tested.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..200

S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001

S. Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki

EXAMPLE

Blazys' expansion of sqrt(2) is {1,2,4,4,4,4,4,...}, i.e., it has a periodic termination. Consequently, 2 is a member of this list.

PROG

(PROG) See the link.

CROSSREFS

Cf. A233593.

Cf. Blazys' expansions: A233582, A233584, A233585, A233586, A233587.

Sequence in context: A167056 A131614 A275202 * A138390 A257804 A285209

Adjacent sequences:  A233589 A233590 A233591 * A233593 A233594 A233595

KEYWORD

nonn

AUTHOR

Stanislav Sykora, Jan 06 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 | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.