|
| |
|
|
A088334
|
|
Expansion of 1/phi (phi being the golden ratio) as an infinite product: 1/phi = prod(k=0,n,1-1/a(k)).
|
|
1
| | |
|
|
|
OFFSET
| 0,1
|
|
|
REFERENCES
| J. Shallit, Problem B-423, The Fibonacci Quarterly 18,1 Feb.(1980)85. Solution 19,1 Febr.(1981) 92. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 04 2010]
|
|
|
FORMULA
| a(0) = 3, a(n+1) = (a(n)-1)*A001566(n+1)
a(n) = 1+ceiling(1/2*(1-1/sqrt(5))*phi^(2^(n+2))) where phi=(1+sqrt(5))/2. a(n)==2 (mod 3) for n>0. - Benoit Cloitre, Nov 09 2003
a(n) = b(n+2)+1, n>=0, with b(n):= A101342(n) = F(2^n-1). See the reciprocal of the infinite product of this entry. For a proof see the J. Shallit reference. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 04 2010]
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, fibonacci(2^(n+2)-1)+1)
|
|
|
CROSSREFS
| Cf. A001566.
Sequence in context: A168590 A081397 A092987 * A050645 A048568 A119678
Adjacent sequences: A088331 A088332 A088333 * A088335 A088336 A088337
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Thomas Baruchel (baruchel(AT)users.sourceforge.net), Nov 07 2003
|
|
|
EXTENSIONS
| The next term is too large to include.
|
| |
|
|
