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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007759 Knopfmacher expansion of sqrt(2): a(2n)=2(a(2n-1)+1)^2 - 1, a(2n+1)=2a(2n)^2 - 2. 0
2, 17, 576, 665857, 886731088896, 1572584048032918633353217, 4946041176255201878775086487573351061418968498176, 48926646634423881954586808839856694558492182258668537145547700898547222910968507268117381704646657 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..8.

A. Knopfmacher and J. Knopfmacher, An alternating product representation for real numbers, in Applications of Fibonacci numbers, Vol. 3 (Kluwer 1990), pp. 209-216.

PROG

(PARI) a(n) = if (n==1, 2, if (n % 2, 2*a(n-1)^2 - 2, 2*(a(n-1)+1)^2 - 1)); \\ Michel Marcus, Feb 20 2019

CROSSREFS

Cf. A002193 (sqrt(2)), A001601.

Sequence in context: A220476 A293178 A172341 * A062710 A012939 A013094

Adjacent sequences:  A007756 A007757 A007758 * A007760 A007761 A007762

KEYWORD

nonn

AUTHOR

Arnold Knopfmacher

EXTENSIONS

More terms from Christian G. Bower, Jan 06 2006

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 June 25 10:10 EDT 2019. Contains 324351 sequences. (Running on oeis4.)