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A273620
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Table read by ascending antidiagonals: T(n, k) = floor(sqrt(k) * floor(n/sqrt(k) + 1)), for n >= 1, k >= 1.
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2
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2, 3, 1, 4, 2, 1, 5, 4, 3, 2, 6, 4, 3, 4, 2, 7, 5, 5, 4, 2, 2, 8, 7, 5, 6, 4, 2, 2, 9, 7, 6, 6, 4, 4, 2, 2, 10, 8, 8, 8, 6, 4, 5, 2, 3, 11, 9, 8, 8, 6, 7, 5, 5, 3, 3, 12, 11, 10, 10, 8, 7, 5, 5, 6, 3, 3, 13, 11, 10, 10, 8, 7, 7, 5, 6, 3, 3, 3, 14, 12, 12, 12
(list;
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refs;
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history;
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OFFSET
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1,1
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COMMENTS
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A261865(n) gives the least k such that T(n, k) = n.
From Peter Kagey, Apr 07 2020: (Start)
T(n, k) is the floor of the least multiple of sqrt(k) that is greater than n.
T(n, k^2) is a multiple of k.
For squarefree k > 1, T(n,k) = n if and only if n appears in column k.
A327952(n) is the number of appearances of n in row n.
(End)
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LINKS
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Peter Kagey, Table of n, a(n) for n = 1..10000
Peter Kagey, A bitmap representing the parity of the first 1023 rows and columns of the sequence. Black pixels represent even values, and white pixels represent odd values.
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FORMULA
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T(n, 1) = n + 1.
T(n, k) = floor(sqrt(k) * floor(n/sqrt(k) + 1)). - Peter Kagey, Apr 07 2020
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EXAMPLE
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A261865(1) = T(1, 1) = floor(sqrt(1) * floor(1/sqrt(1) + 1)) = 2
A261865(2) = T(2, 1) = floor(sqrt(1) * floor(1/sqrt(2) + 1)) = 1
A261865(3) = T(1, 2) = floor(sqrt(2) * floor(2/sqrt(1) + 1)) = 4
Table begins:
n\k | 1 2 3 4 5 6 7 8 9 10
----+------------------------------
1| 2 1 1 2 2 2 2 2 3 3
2| 3 2 3 4 2 2 2 2 3 3
3| 4 4 3 4 4 4 5 5 6 3
4| 5 4 5 6 4 4 5 5 6 6
5| 6 5 5 6 6 7 5 5 6 6
6| 7 7 6 8 6 7 7 8 9 6
7| 8 7 8 8 8 7 7 8 9 9
8| 9 8 8 10 8 9 10 8 9 9
9| 10 9 10 10 11 9 10 11 12 9
10| 11 11 10 12 11 12 10 11 12 12
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MATHEMATICA
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Table[Function[j, Floor[Sqrt@ k Floor[j/Sqrt@ k + 1]]][n - k + 1], {n, 13}, {k, n}] // Flatten (* Michael De Vlieger, May 27 2016 *)
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PROG
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(Haskell)
a273620T :: Integral a => a -> a -> a
a273620T n k = floor $ sqrt k' * c where
(n', k') = (fromIntegral n, fromIntegral k)
c = fromIntegral $ floor $ n' / sqrt k' + 1
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CROSSREFS
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The first column consists of entries in A001951, the second column of entries in A022838, the fourth of entries in A022839, and the fifth of entries in A022840.
Cf. A261865, A327952.
Sequence in context: A087088 A336811 A255250 * A104705 A143361 A152547
Adjacent sequences: A273617 A273618 A273619 * A273621 A273622 A273623
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Kagey, May 26 2016
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STATUS
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approved
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