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

Author

N. J. A. Sloane, Dec 03 2004

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A250007 (run lengths).

Programs

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

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 *)