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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A165116 A111656

Adjacent sequences:  A100614 A100615 A100616 * A100618 A100619 A100620

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Dec 03 2004

STATUS

approved

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Last modified December 8 12:55 EST 2016. Contains 278945 sequences.