A125153 The interspersion T(3,2,1), by antidiagonals.

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

Offset

1,2

Comments

Every positive integer occurs exactly once and each pair of rows are interspersed after initial terms.

References

Clark Kimberling, Interspersions and fractal sequences associated with fractions (c^j)/(d^k), Journal of Integer Sequences 10 (2007, Article 07.5.1) 1-8.

Links

Table of n, a(n) for n=1..55.

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: A167557 A069836 A224820 * A191451 A193950 A180194

Adjacent sequences: A125150 A125151 A125152 * A125154 A125155 A125156

Keyword

nonn,tabl

Author

Clark Kimberling, Nov 21 2006

Status

approved