OFFSET
0,2
COMMENTS
LINKS
Andrew N. W. Hone, Curious continued fractions, nonlinear recurrences and transcendental numbers, arXiv:1507.00063 [math.NT], 2015 and J. Int. Seq. 18 (2015) # 15.8.4.
FORMULA
a(n) = a(n-1)*(1 + a(0)*a(1)*a(2)*...*a(n-1)) for n>=1, with a(0)=1.
a(n) = a(n-1)*(1 - a(n-1) + a(n-1)^2/a(n-2)) for n>=2, with a(0)=1, a(1)=2.
EXAMPLE
a(5) = 4999703411742 = 73086*(1 + 1*2*6*78*73086).
a(5) = a(4)*(1 - a(4) + a(4)^2/a(3)) = 73086*(1 - 73086 + 73086^2/78).
PROG
(PARI) a(n)=if(n==0, 1, if(n==1, 2, a(n-1)*(1-a(n-1)+a(n-1)^2/a(n-2))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 08 2005
EXTENSIONS
a(7) corrected by Georg Fischer, Aug 26 2022
STATUS
approved