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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 (list; table; graph; refs; listen; history; text; internal format)
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, 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.

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.

Cf. A261865, A327952.

Sequence in context: A087088 A336811 A255250 * A104705 A143361 A152547

Adjacent sequences:  A273617 A273618 A273619 * A273621 A273622 A273623

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, May 26 2016

STATUS

approved

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Last modified June 26 12:41 EDT 2022. Contains 354883 sequences. (Running on oeis4.)