A125150 The interspersion T(2,3,0), by antidiagonals.

1, 2, 3, 4, 7, 5, 8, 14, 10, 6, 16, 28, 21, 12, 9, 32, 56, 42, 25, 18, 11, 64, 113, 85, 50, 37, 22, 13, 128, 227, 170, 101, 75, 44, 26, 15, 256, 455, 341, 202, 151, 89, 53, 31, 17, 512, 910, 682, 404, 303, 179, 106, 63, 35, 19, 1024, 1820, 1365, 809, 606, 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)=2^(h-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=(2^4)/(3^1), where 5=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 LPI 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 4 8 16 32 64
3 7 14 28 56 113 227
5 10 21 42 85 170 341
6 12 25 50 101 202 404
9 18 37 75 151 303 606

Crossrefs

Cf. A125154, A125158.

Sequence in context: A026237 A308301 A357578 * A265901 A257801 A257726

Adjacent sequences: A125147 A125148 A125149 * A125151 A125152 A125153

Keyword

nonn,tabl

Author

Clark Kimberling, Nov 21 2006

Status

approved