A100617 - OEIS

%I #28 Nov 24 2016 09:27:20

%S 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,

%T 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,

%U 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

%N 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.

%D 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.

%H Reinhard Zumkeller, <a href="/A100617/b100617.txt">Table of n, a(n) for n = 1..10000</a>

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

%F For all n >= 1, a(A000960(n)) = n. [From above.] - _Antti Karttunen_, Nov 23 2016

%e 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.

%p 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;

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

%o (Haskell)

%o a100617 = f 2 where

%o    f k x = if x' == 0 then x else f (k + 1) (x - x') where x' = div x k

%o -- _Reinhard Zumkeller_, Jul 01 2013, Sep 15 2011

%o (Scheme, with my IntSeq-library)

%o (define A100617 (LEFTINV-LEASTMONO 1 1 A000960))

%o ;; _Antti Karttunen_, Nov 23 2016

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

%Y Cf. A100618.

%Y Cf. A056526 (run lengths).

%K nonn,nice

%O 1,3

%A _N. J. A. Sloane_, Dec 03 2004