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A300691
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).
1
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
OFFSET
1,3
COMMENTS
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.
FORMULA
T(1, k) = k.
T(2, k) = k.
T(3, k) = A300669(k).
T(n, 1) = A300428(n).
T(n, k) = n for some k iff n belongs to A000079 or to A153055.
T(A000225(i), k) = T(2*A000225(i), k) for any i > 0.
EXAMPLE
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
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Mar 11 2018
STATUS
approved