A125151 The interspersion T(2,3,1), by antidiagonals.

1, 2, 3, 5, 7, 4, 10, 14, 9, 6, 21, 28, 18, 12, 8, 42, 56, 37, 25, 16, 11, 85, 113, 75, 50, 33, 22, 13, 170, 227, 151, 101, 67, 44, 26, 15, 341, 455, 303, 202, 134, 89, 53, 31, 17, 682, 910, 606, 404, 269, 179, 106, 63, 35, 19, 1365, 1820, 1213, 809, 539, 359, 213, 126

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..63.

C. Kimberling, Interspersions and Dispersions.

Formula

Row 1: t(1,h)=Floor[r*2^(h-1)], where r=(2^2)/(3^1), h=1,2,3,... Row 2: t(2,h)=Floor[r*2^(h-1)], r=(2^5)/(3^2), where 3=Floor[r] is least positive integer (LPI) not in row 1. Row 3: t(3,h)=Floor[r*2^(h-1)], r=(2^7)/(3^3), where 4=Floor[r] is the LPI not in rows 1 and 2. Row m: t(m,h)=Floor[r*2^(h-1)], where r=(2^j)/(3^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 2 5 10 21 42 85
3 7 14 28 56 113 227
4 9 18 37 75 151 303
6 12 25 50 101 202 404
8 16 33 67 134 269 539

Crossrefs

Cf. A125155, A125159.

Sequence in context: A284145 A284189 A114319 * A372130 A302024 A273665

Adjacent sequences: A125148 A125149 A125150 * A125152 A125153 A125154

Keyword

nonn,tabl

Author

Clark Kimberling, Nov 21 2006

Status

approved