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A300691
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Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number, say m, such that the binary representation of n appears as a substring in the binary representation of 1/m (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion).
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1
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1, 1, 2, 5, 2, 3, 1, 9, 3, 4, 3, 2, 10, 4, 5, 5, 6, 4, 11, 5, 6, 9, 9, 11, 5, 13, 6, 7, 1, 11, 10, 12, 7, 17, 7, 8, 5, 2, 13, 11, 13, 8, 18, 8, 9, 3, 7, 4, 17, 13, 19, 9, 19, 9, 10, 11, 6, 10, 8, 18, 17, 22, 10, 20, 10, 11, 5, 13, 11, 13, 9, 19, 18, 23, 11, 21
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OFFSET
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1,3
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COMMENTS
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If m appears in the n-th row, then 2*m also appears in the n-th row.
This array has connections with A300653: here n appears in 1/T(n, k), there T(n, k) appears in 1/n.
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LINKS
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FORMULA
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T(1, k) = k.
T(2, k) = k.
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EXAMPLE
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Square array begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12
---+------------------------------------------------
1| 1 2 3 4 5 6 7 8 9 10 11 12 --> A000027
2| 1 2 3 4 5 6 7 8 9 10 11 12 --> A000027
3| 5 9 10 11 13 17 18 19 20 21 22 23 --> A300669
4| 1 2 4 5 7 8 9 10 11 13 14 15
5| 3 6 11 12 13 19 22 23 24 25 26 27
6| 5 9 10 11 13 17 18 19 20 21 22 23
7| 9 11 13 17 18 19 22 25 26 27 29 33
8| 1 2 4 8 9 11 13 15 16 17 18 19
9| 5 7 10 13 14 19 20 23 26 27 28 29
10| 3 6 11 12 19 22 24 25 27 29 35 37
11| 11 13 19 22 23 25 26 27 29 37 38 43
12| 5 9 10 13 17 18 19 20 21 23 25 26
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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