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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A192222 a(n) = Fibonacci(2^n + 1). 5
 1, 2, 5, 34, 1597, 3524578, 17167680177565, 407305795904080553832073954, 229265413057075367692743352179590077832064383222590237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Jonathan Sondow, Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, Vol. 1385, No. 1 (2011), pp. 97-100, arXiv preprint, arXiv:1106.4246 [math.NT], 2011. Yohei Tachiya, Transcendence of certain infinite products, J. Number Theory, Vol. 125, No. 1 (2007), pp. 182-200. FORMULA a(n) = A000045(2^n + 1). Product_{n>0} (1 + 1/a(n)) = 3/phi = A134973, where phi = (1+sqrt(5))/2 is the golden mean. Sum_{n>=0} 1/a(n) = A338305. - Amiram Eldar, Oct 22 2020 MATHEMATICA Table[Fibonacci[2^n + 1], {n, 0, 10}] (* T. D. Noe, Jan 11 2012 *) CROSSREFS Cf. A000045 (Fibonacci numbers F(n)), A001622, A134973 (decimal expansion of 3/phi), A192223 (Lucas(2^n + 1)), A338305. Sequence in context: A206830 A277436 A002665 * A326946 A241586 A000665 Adjacent sequences:  A192219 A192220 A192221 * A192223 A192224 A192225 KEYWORD nonn,easy 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.

Last modified April 11 08:10 EDT 2021. Contains 342886 sequences. (Running on oeis4.)