|
Search: id:A071766
|
|
|
| A071766 |
|
Denominator of the continued fraction expansion whose terms are the first-order differences of exponents in the binary representation of 4*n, with the exponents of 2 being listed in descending order. |
|
+0
6
|
|
| 1, 1, 1, 2, 1, 2, 3, 3, 1, 2, 3, 3, 4, 5, 4, 5, 1, 2, 3, 3, 4, 5, 4, 5, 5, 7, 7, 8, 5, 7, 7, 8, 1, 2, 3, 3, 4, 5, 4, 5, 5, 7, 7, 8, 5, 7, 7, 8, 6, 9, 10, 11, 9, 12, 11, 13, 6, 9, 10, 11, 9, 12, 11, 13, 1, 2, 3, 3, 4, 5, 4, 5, 5, 7, 7, 8, 5, 7, 7, 8, 6, 9, 10, 11, 9, 12, 11, 13
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
FORMULA
|
a(n) = A071585(m), where m = n - floor(log(n)/log(2)); A(0) = 1, A(2^k) = 1, A(2^k + 1) = 2, A(2^k - 1) = k-th Fibonacci number.
|
|
EXAMPLE
|
a(37)=5 as it is the denominator of 17/5 = 3 + 1/(2 + 1/2), which is a continued fraction that can be derived from the binary expansion of 4*37 = 2^7 + 2^4 + 2^2; the binary exponents are {7, 4, 2}, thus the differences of these exponents are {3, 2, 2}; giving the continued fraction expansion of 17/5=[3,2,2].
|
|
CROSSREFS
|
Cf. A071585.
Sequence in context: A033803 A035531 A118977 this_sequence A007305 A112531 A100002
Adjacent sequences: A071763 A071764 A071765 this_sequence A071767 A071768 A071769
|
|
KEYWORD
|
easy,nonn,frac
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jun 04 2002
|
|
|
Search completed in 0.002 seconds
|
