

A100617


There are n people in a room. First half (i.e. [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.


4



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
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OFFSET

1,3


REFERENCES

V. Brun, Un proc\'{e}d\'{e} qui ressemble au crible d'Eratosthene, Analele Stiintifice Univ. "Al. I. Cuza", Iasi, Romania, Sect. Ia Matematica, 1965, vol. 11B, pp. 4753.


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).


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 := kj; od; k; end;


MATHEMATICA

a[n_] := (k = 2; FixedPoint[#  Floor[# / k++]&, n]); Table[a[n], {n, 1, 96}] (* JeanFrançois 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


CROSSREFS

Cf. A000960, A100618.
Cf. A056526 (run lengths).
Sequence in context: A000194 A168255 A097429 * A076471 A165116 A111656
Adjacent sequences: A100614 A100615 A100616 * A100618 A100619 A100620


KEYWORD

nonn,nice,changed


AUTHOR

N. J. A. Sloane, Dec 03 2004


STATUS

approved



