

A273620


Table read by antidiagonals: T(n, k) = floor(sqrt(k) * floor(n/sqrt(k) + 1)) with 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
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OFFSET

1,1


COMMENTS

A261865(n) gives the least k such that T(n, k) < n + 1.
T(n, 1) = n + 1.


LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000


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


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

Cf. A261865.
Sequence in context: A223025 A087088 A255250 * A104705 A143361 A152547
Adjacent sequences: A273617 A273618 A273619 * A273621 A273622 A273623


KEYWORD

nonn,tabl


AUTHOR

Peter Kagey, May 26 2016


STATUS

approved



