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A125151
The interspersion T(2,3,1), by antidiagonals.
2
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.
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
Sequence in context: A284189 A373999 A114319 * A372130 A302024 A273665
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 21 2006
STATUS
approved