|
Search: id:A109054
|
|
|
| A109054 |
|
Numbers n such that the continued fraction expansion of sqrt(n) is multiplicative. |
|
+0
2
|
|
| 0, 1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 22, 23, 24, 25, 32, 33, 34, 35, 36, 44, 47, 48, 49, 58, 59, 60, 62, 63, 64, 74, 75, 78, 79, 80, 81, 95, 96, 98, 99, 100, 114, 119, 120, 121, 135, 136, 138, 140, 141, 142, 143, 144, 160, 162, 164, 167, 168, 169, 185, 187, 189, 192
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Perfect squares are assumed to have a continued fraction expansion of all zeros after a(0) and so are trivially multiplicative
For nonsquares, a(1) must be 1, and so n must satisfy k+1/2 < sqrt(n) <= k+1, for some integer k.
|
|
EXAMPLE
|
The continued fraction of sqrt(22) is (4; 1, 2, 4, 2, 1, 8, ...), which is multiplicative with a(2^e) = 2, a(3^e) = 4, a(p^e) = 1 otherwise.
|
|
CROSSREFS
|
Cf. A040001, A010121, A040005, etc.
Sequence in context: A110133 A100452 A004201 this_sequence A129142 A075752 A046541
Adjacent sequences: A109051 A109052 A109053 this_sequence A109055 A109056 A109057
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jun 18 2005
|
|
|
Search completed in 0.002 seconds
|
