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!)
A162924 Denominators of fractions converging to square root 3 satisfying: a(n)=1/a(n-1)+1/a(n-2)+ 1/a(n-3) or numerators of reciprocal satisfying: a(n)=1/(a(n-1)+ a(n-2)+ a(n-3)) with a(1,2,3)= 1 3
1, 1, 1, 1, 3, 21, 777, 267547, 17878140297, 16341834244642095861, 478987257940772584908938949874389249, 804559699103199797086217986081816861067730765554524831136628441253 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
For other square roots of positive integers add or subtract more a(n) to formula and start off.
LINKS
EXAMPLE
For n=5 a(5)= 1/1 + 1/1 + 1/3 = 7/3 (denominator) For n=5 a(5)= 1/(1 + 1 + 1/3) = 3/7 (numerator)
MATHEMATICA
nxt[{a_, b_, c_}]:={b, c, 1/a+1/b+1/c}; Denominator[Transpose[NestList[nxt, {1, 1, 1}, 15]][[1]]] (* Harvey P. Dale, Dec 09 2012 *)
CROSSREFS
Cf. A162926 (numerators). A066932, A057677
Sequence in context: A291967 A171104 A057600 * A079269 A127104 A176430
KEYWORD
nonn,frac
AUTHOR
Mark Dols, Jul 17 2009
EXTENSIONS
More terms from Harvey P. Dale, Dec 09 2012
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 19 14:50 EDT 2024. Contains 373503 sequences. (Running on oeis4.)