A250007 -id:A250007 - cp's OEIS frontend

A056526 First differences of Flavius Josephus's sieve.

2, 4, 6, 6, 8, 12, 10, 14, 16, 12, 18, 24, 14, 34, 26, 16, 30, 36, 18, 42, 38, 12, 60, 22, 48, 38, 46, 36, 60, 54, 44, 36, 84, 22, 60, 84, 18, 78, 72, 60, 38, 112, 12, 96, 114, 26, 88, 92, 34, 90, 138, 26, 82, 98, 112, 54, 170, 36, 60, 168, 52, 128, 52, 128, 94, 108, 90, 188

Offset: 1

Henry Bottomley, Jun 16 2000

nonn

Also run lengths in A100617. - Reinhard Zumkeller, Jan 14 2015

			Flavius's sieve starts 1,3,7,13,19,27,39,49 so first differences are 2,4,6,6,8,12,10.

Klaus Brockhaus, Table of n, a(n) for n=1..10000
Index entries for sequences related to the Josephus Problem

Cf. A000960 for definition, A139363 (records), A139364 (where records occur).

Cf. A100617, A250007.

a056526 n = a056526_list !! (n-1)
a056526_list = zipWith (-) (tail a000960_list) a000960_list
-- Reinhard Zumkeller, Jan 14 2015

a(n) = A000960(n+1) - A000960(n).

A100618 Initially there are n people in a room. At each step, if there are currently M people in the room, [M/k^2] of them leave, for k = 2, 3, ... Sequence gives number who are left at the end.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 23, 23, 24, 24, 25, 25, 26, 27, 28, 28, 29, 29, 29, 29, 30, 31, 32, 32, 33, 34, 35, 35, 35, 36, 36, 36, 37, 38, 39, 39, 40, 41, 42, 42, 43, 43, 43, 43, 44, 45, 46, 46

Offset: 1

N. J. A. Sloane, Dec 03 2004

nonn

If [M/k^2] is changed to [M/k] we get A100617.

			10 -> 10 - [10/4] = 8 -> 8 - [8/9] = 8, which is now fixed, so a(10) = 8.

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

Cf. A250007 (run lengths).

a100618 n = f 2 n where
   f k n | n' == 0   = n
         | otherwise = f (k+1) (n-n') where n' = div n (k^2)
-- Reinhard Zumkeller, Sep 15 2011

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

a[n_] := (k = 2; FixedPoint[# - Floor[#/(k++)^2]&, n]); Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 10 2018 *)

cp's OEIS Frontend

A056526 First differences of Flavius Josephus's sieve.

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