A100618 Initially there are n people in a room. At each step, if there are currently M people in the room, [M/k^2] of them leave, for k = 2, 3, ... Sequence gives number who are left at the end.

1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 23, 23, 24, 24, 25, 25, 26, 27, 28, 28, 29, 29, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 35, 36, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 43, 43, 43, 44, 45, 46, 46

Offset

1,2

Comments

If [M/k^2] is changed to [M/k] we get A100617.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

10 -> 10 - [10/4] = 8 -> 8 - [8/9] = 8, which is now fixed, so a(10) = 8.

Maple

f:=proc(n) local i, j, k; k:=n; for i from 2 to 10000 do j := floor(k/(i^2)); if j < 1 then break; fi; k := k-j; od; k; end;

Mathematica

a[n_] := (k = 2; FixedPoint[# - Floor[#/(k++)^2]&, n]); Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 10 2018 *)

Prog

(Haskell)
a100618 n = f 2 n where
   f k n | n' == 0   = n
         | otherwise = f (k+1) (n-n') where n' = div n (k^2)
-- Reinhard Zumkeller, Sep 15 2011

Crossrefs

Cf. A250007 (run lengths).

Sequence in context: A091245 A347649 A368908 * A248227 A061288 A086525

Adjacent sequences: A100615 A100616 A100617 * A100619 A100620 A100621

Keyword

nonn

Author

N. J. A. Sloane, Dec 03 2004

Status

approved