|
| |
|
|
A132223
|
|
A dense infinitive sequence.
|
|
3
| |
|
|
1, 2, 1, 4, 2, 3, 1, 8, 4, 7, 2, 6, 3, 5, 1, 16, 8, 15, 4, 14, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9, 1, 32, 16, 31, 8, 30, 15, 29, 4, 28, 14, 27, 7, 26, 13, 25, 2, 24, 12, 23, 6, 22, 11, 21, 3, 20, 10, 19, 5, 18, 9, 17
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| The sequence is dense in the sense that any two neighboring terms in a segment are separated in all succeeding segments. Thus in the limiting para-sequence, each pair of positive integers are separated by infinitely many positive integers.
A sequence is an infinitive sequence if and only if it is a sequence that contains every positive integer and also contains itself as a proper subsequence.
See A132224 for the normalization of A132223, making A132224 a fractal sequence.
|
|
|
REFERENCES
| C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n = 1..8190 (12 segments)
|
|
|
FORMULA
| Start with 1,2. Separate them by 3,4, like this: 1,4,2,3. Then separate those by 5,6,7,8 like this: 1,8,4,7,2,6,3,5. Continue the process. Regard 1,2 and 1,4,2,3 and 1,8,4,7,2,6,3,5 as successive segments, so that the n-th segment has 2^n terms.
|
|
|
EXAMPLE
| The next segment after 1,8,4,7,2,6,3,5, formed by separating those by 9,10,11,12,13,14,15,16, is 1,16,8,15,4,14,7,13,2,12,6,11,3,10,5,9.
|
|
|
MATHEMATICA
| Flatten@FoldList[Riffle[#1, Range[2^#2, 2^(#2 - 1) + 1, -1]] &, {1, 2}, Range[2, 5]] (* Gyorgy Birkas, Apr 20, 2011 *)
|
|
|
CROSSREFS
| Cf. A132224.
Sequence in context: A123755 A118291 A118290 * A135941 A036998 A121464
Adjacent sequences: A132220 A132221 A132222 * A132224 A132225 A132226
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Aug 14 2007
|
| |
|
|
