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

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192222 Fibonacci(2^n + 1). 4
1, 2, 5, 34, 1597, 3524578, 17167680177565, 407305795904080553832073954, 229265413057075367692743352179590077832064383222590237 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Product_{n>0} (1 + 1/a(n)) = 3/phi = A134973, where phi = (1+sqrt(5))/2 is the golden mean.

LINKS

Table of n, a(n) for n=0..8.

J. Sondow, Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, vol. 1385, pp. 97-100.

Y. Tachiya, Transcendence of certain infinite products, J. Number Theory 125 (2007), 182-200.

FORMULA

a(n) = A000045(2^n + 1).

MATHEMATICA

Table[Fibonacci[2^n + 1], {n, 0, 10}] (* T. D. Noe, Jan 11 2012 *)

CROSSREFS

Cf. A000045 (Fibonacci numbers F(n)), A134973 (decimal expansion of 3/phi), A192223 (Lucas(2^n + 1)).

Sequence in context: A206830 A277436 A002665 * A241586 A000665 A058882

Adjacent sequences:  A192219 A192220 A192221 * A192223 A192224 A192225

KEYWORD

nonn,easy,changed

AUTHOR

Jonathan Sondow, Jun 26 2011

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 December 17 14:12 EST 2018. Contains 318201 sequences. (Running on oeis4.)