|
Search: id:A125153
|
|
|
| A125153 |
|
The interspersion T(3,2,1), by antidiagonals. |
|
+0
3
|
|
| 1, 4, 2, 13, 6, 3, 40, 20, 10, 5, 121, 60, 30, 15, 7, 364, 182, 91, 45, 22, 8, 1093, 546, 273, 136, 68, 25, 9, 3280, 1640, 820, 410, 205, 76, 28, 11, 9841, 4920, 2460, 1230, 615, 230, 86, 34, 12, 29524, 14762, 7381, 3690, 1845, 691, 259, 102, 38, 14
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Every positive integer occurs exactly once and each pair of rows are interspersed after initial terms.
|
|
REFERENCES
|
C. Kimberling, "Interspersions and fractal sequences associated with fractions (c^j)/(d^k)," preprint, 2006.
|
|
LINKS
|
C. Kimberling, Interspersions and Dispersions.
|
|
FORMULA
|
Row 1: t(1,h)=Floor[r*3^(h-1)], where r=(3^1)/(2^1), h=1,2,3,... Row 2: t(2,h)=Floor[r*3^(h-1)], r=(3^2)/(2^2), where 2=Floor[r] is least positive integer (LPI) not in row 1. Row 3: t(3,h)=Floor[r*3^(h-1)], r=(3^3)/(2^3), where 3=Floor[r] is the LPI not in rows 1 and 2. Row m: t(m,h)=Floor[r*3^(h-1)], where r=(3^j)/(2^k), where k is the least integer >=1 for which there is an integer j for which the LPI not in rows 1,2,...,m-1 is Floor[r].
|
|
EXAMPLE
|
Northwest corner:
1 4 13 40 121 364 1093
2 6 20 60 182 546 1640
3 10 30 91 273 820 2460
5 15 45 136 410 1230 3690
7 22 68 205 615 1845 5535
|
|
CROSSREFS
|
Cf. A125157, A125161.
Sequence in context: A105196 A167557 A069836 this_sequence A096034 A064308 A161134
Adjacent sequences: A125150 A125151 A125152 this_sequence A125154 A125155 A125156
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), Nov 21 2006
|
|
|
Search completed in 0.002 seconds
|
