login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 2
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

Harvey P. Dale, Table of n, a(n) for n = 1..16

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

Adjacent sequences:  A162921 A162922 A162923 * A162925 A162926 A162927

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 01:33 EST 2020. Contains 331229 sequences. (Running on oeis4.)