|
| |
|
|
A114309
|
|
Lexicographically earliest sequence which has the property that it lists the position of the even digits in the concatenation of its terms.
|
|
1
| |
|
|
3, 5, 6, 7, 8, 20, 21, 31, 33, 35, 37, 39, 40, 51, 53, 55, 57, 58, 70, 72, 74, 76, 81, 91, 93, 95, 97, 98, 101, 210, 211, 311, 313, 315, 410, 501, 611, 710, 711, 713, 715, 810, 901, 2011, 2111, 3111, 3113, 3115, 3117, 3119, 3131, 3133, 3135, 3137, 3139, 3151, 3153
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| A self-describing sequence. See the sequence as a succession of digits: then a(n) is the position of the even digits of the sequence.
"Lexicographically earliest" refers to comparing sequences term by term, not the strings obtained by the concatenation. (This is not possible, since then the first term could be an arbitrarily long string of 1's.) In other words, term after term, the smallest possible value not leading to a contradiction is appended.
|
|
|
EXAMPLE
| We can't have a(1)=1 (since then the first digit would not be even) nor a(1)=2 (since then the first digit would be even), but a(1)=3 is possible.
This implies that there follows another odd digit, a(2)=5, before the first even digit a(a(1))=a(3)=6.
Then comes another odd digit, a(4)=7, since the second even digit occurs only in position a(2)=5, namely a(5)=8.
______________________ 1 _________________ 2 _________________ 3 _ ...
pos. 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 ...
seq. 3,5,6,7,8,2 0,2 1,3 1,3 3,3 5,3 7,3 9,4 0,5 1,5 3,5 5,5 7,5 8,...
The even digits of the sequence are between parentheses here:
Sequence: 3,5,(6),7,(8),(2)(0),(2)1,31,33,35,37,39,(4)(0)...
Positions of even digits: 3, 5, 6, 7, 8, 20, 21... = the sequence itself
|
|
|
CROSSREFS
| Sequence in context: A159559 A047583 A010906 * A079581 A057716 A138591
Adjacent sequences: A114306 A114307 A114308 * A114310 A114311 A114312
|
|
|
KEYWORD
| base,easy,nonn,nice
|
|
|
AUTHOR
| Eric Angelini (eric.angelini(AT)kntv.be), Feb 05 2006
|
|
|
EXTENSIONS
| Edited by M. F. Hasler, Dec 06 2009
Further edits by N. J. A. Sloane, Dec 19 2009
More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), May 05 2010
|
| |
|
|
