This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A122579 Integer sequence arising from the nested radical R(m)=sqrt(4^0+sqrt(4^1+sqrt(....+sqrt(4^m)...) (see comment). 0
 1, 1, 3, 15, 455, 53175, 52802967, 194817927511, 3103080851583191, 200041552904055799767, 52027813627693614618566103, 54341050032531342541499355961815 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let p(k)=prod(i=0,k,2^i+1) (A028361) then for any n>0 we get the asymptotic formula as m-->infty : 2-R(m)=a(0)*(1/p(m))+a(1)*(2/p(m+1))+...+a(n)*(2^n/p(m+n))+O(1/p(m+n+1)). In particular there is this unexpected relation between an infinite nested radical and an infinite product : limit m-->infty (2-R(m))*2^(m*(m+1)/2)=1/prod(i>=0,1+1/2^i)=0.29.... (A083864). REFERENCES B. Cloitre, On an asymptotic formula for a nested radical, in preparation 2006 LINKS FORMULA a(n) is asymptotic to c*4^(n*(n-1)/2) for c=0.041.... CROSSREFS Cf. A028361, A083864. Sequence in context: A296940 A193119 A309069 * A138303 A267096 A217449 Adjacent sequences:  A122576 A122577 A122578 * A122580 A122581 A122582 KEYWORD nonn AUTHOR Benoit Cloitre, Oct 29 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.

Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)