|
| |
|
|
A084764
|
|
a(n)=2a(n-1)^2-1, a(0)=1, a(1)=4.
|
|
1
| | |
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| Product((1+1/a(k)), k=1,..,n) converges to sqrt(5/3).
|
|
|
REFERENCES
| H. S. Wilf, Limit of a sequence, Elementary Problem E 1093, Amer. Math. Monthly 61 (1954), 424-425
|
|
|
LINKS
| J. O. Shallit, Rational numbers with non-terminating, non-periodic modified Engel-type expansions, Fib. Quart., 31 (1993), 37-40.
|
|
|
FORMULA
| With a=4+sqrt(15), b=4-sqrt(15): a(n+1)=(a^(2^n)+b^(2^n))/2.
a(n)=A005828(n-1), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2008]
|
|
|
MATHEMATICA
| For n>0: b[n_] := b[n] = 2 b[n - 1]^2 - 1; b[1] = 4 Table[b[n], {n, 1, 8}]
|
|
|
CROSSREFS
| Sequence in context: A203011 A005841 A005828 * A061789 A103909 A196247
Adjacent sequences: A084761 A084762 A084763 * A084765 A084766 A084767
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Mario Catalani (mario.catalani(AT)unito.it), Jun 04 2003
|
| |
|
|
