|
Search: id:A131989
|
|
|
| A131989 |
|
Start with the symbol **|* and for each iteration replace * with **|*. This sequence is the number of *'s between each dash. |
|
+0
2
|
|
| 2, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 1, 2, 3, 1, 2, 3, 3, 1, 2, 3
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
If the leading a(1)=2 is dropped, at least the next 90 terms coincide with those of A026181. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl(, Jun 13 2008
|
|
FORMULA
|
Comments from njas, Oct 10 2007: (Start) The following is a simple recursive method to generate this sequene. The sequence is lim_{ t -> oo } S_t, where S_0 = 1+,
and S_{t+1} is obtained from the concatenation S_t S_t S_t by replacing the first +
by the sum of the two numbers adjacent to it and deleting the second +.
Thus we have:
S_0 = 1+,
S_1 = 1+1+1+ -> 21+,
S_2 = 21+21+21+ -> 23121+,
S_3 = 23121+23121+23121+ -> 23123312123121+,
S_4 = 23123312123121+23123312123121+23123312123121+ -> 23123312123123312331212312123123312123121+, etc.
Denote the sequence by a(1), a(2), ...
Block t, that is, S_t omitting the final 1+, extends from n=1 through n=(3^t-1)/2.
Given n, to find a(n): first find t from
p = (3^(t-1)-1)/2 < n <= (3^t-1)/2.
Assume t >= 2. Then if n=(3^(t-1)+1)/2, a(n) = 3 and if n=3^(t-1), a(n) = 1.
Otherwise, a(n) = a(n'), where
n' = n-p if n<3^(t-1), otherwise n' = n-3^(t-1). (End)
|
|
EXAMPLE
|
The symbol through a few iterations: **|*, **|***|*|**|*, **|***|*|**|***|***|*|**|*|**|***|*|**|*, etc.
|
|
CROSSREFS
|
a(n) = length of n-th run of 1's in A133162. - njas, Oct 09 2007
Sequence in context: A105933 A105315 A130830 this_sequence A065365 A096137 A063274
Adjacent sequences: A131986 A131987 A131988 this_sequence A131990 A131991 A131992
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Alex H. Bishop (AlexanderBishop(AT)stmarksschool.org), Oct 07 2007
|
|
EXTENSIONS
|
More terms from njas, Oct 10 2007
|
|
|
Search completed in 0.002 seconds
|
