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A273620
Table read by ascending antidiagonals: T(n, k) = floor(sqrt(k) * floor(n/sqrt(k) + 1)), for n >= 1, k >= 1.
2
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
OFFSET
1,1
COMMENTS
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)
LINKS
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.
FORMULA
T(n, 1) = n + 1.
T(n, k) = floor(sqrt(k) * floor(n/sqrt(k) + 1)). - Peter Kagey, Apr 07 2020
EXAMPLE
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
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.
Sequence in context: A087088 A336811 A255250 * A104705 A143361 A152547
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, May 26 2016
STATUS
approved