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

1,3

References

V. Brun, Un procédé qui ressemble au crible d'Eratosthene, 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

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

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A100618.

Cf. A056526 (run lengths).

Sequence in context: A000194 A168255 A097429 * A076471 A339391 A165116

Adjacent sequences: A100614 A100615 A100616 * A100618 A100619 A100620

Keyword

nonn,nice

Author

N. J. A. Sloane, Dec 03 2004

Status

approved