A100617 There are n people in a room. The first half (i.e., floor(n/2)) of them leave, then 1/3 (i.e., floor of 1/3) of those remaining leave, then 1/4, then 1/5, etc.; sequence gives number who remain at the end.

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11

Offset: 1

Author

N. J. A. Sloane, Dec 03 2004

Keywords

• nonn
• nice

Examples

			7 -> 7 - [7/2] = 7 - 3 = 4 -> 4 - [4/3] = 4 - 1 = 3 -> 3 - [3/4] = 3 - 0 = 3, which is now fixed, so a(7) = 3.
		

References

• V. Brun, Un procédé qui ressemble au crible d'Ératosthène, Analele Stiintifice Univ. "Al. I. Cuza", Iasi, Romania, Sect. Ia Matematica, 1965, vol. 11B, pp. 47-53.

Links

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

Crossrefs

Least monotonic left inverse of A000960, partial sums of A278169.

Cf. A100618.

Cf. A056526 (run lengths).

Programs

Haskell

a100617 = f 2 where
   f k x = if x' == 0 then x else f (k + 1) (x - x') where x' = div x k
-- Reinhard Zumkeller, Jul 01 2013, Sep 15 2011

Maple

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

Mathematica

a[n_] := (k = 2; FixedPoint[# - Floor[# / k++]&, n]); Table[a[n], {n, 1, 96}] (* Jean-François Alcover, Nov 15 2011 *)

Scheme

;; With my IntSeq-library.
(define A100617 (LEFTINV-LEASTMONO 1 1 A000960))
;; Antti Karttunen, Nov 23 2016

Formula

a(n) = k for Fl(k) <= n < Fl(k+1), where Fl(i) = A000960(i).

For all n >= 1, a(A000960(n)) = n. [From above.] - Antti Karttunen, Nov 23 2016