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A247105 Variation of Flavius Josephus's sieve: Start with the natural numbers; at the k-th sieving step, make k passes removing every k-th term of the sequence remaining after the previous sieving step; iterate. 1
1, 5, 25, 109, 385, 1373, 4645, 16009, 48817, 159757, 488377, 1571425, 4560901, 14482393, 43408013, 130394125, 380755429, 1118740741, 3326930413, 9931863461, 28466058257, 84243573797, 240453967777, 706827067045, 2009065808473, 5913933615149, 16711898903281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Starting with the natural numbers, make 2 passes removing every 2nd number, 3 passes removing every 3rd number, etc.

Is the limiting value of a(n+1)/a(n)=3?

Since 1/(1-1/n)^n converges to e (as n -> inf), a(n+1)/a(n) converges to e. - Hiroaki Yamanouchi, Nov 27 2014

LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..1000

Index entries for sequences related to the Josephus Problem

EXAMPLE

The 1st pass removes 2, 4, 6, 8, 10, etc. The 2nd pass (also with 2) removes 3, 7, 11, 15, 19, etc. Then there are 3 passes removing every 3rd number, of which the 1st pass removes 9, 21, 33, 45, ..., the 2nd removes 13, 29, 49, ..., and the 3rd removes 17, 41, 73, ...; then there are 4 passes with 4; 5 passes with 5; etc.

MATHEMATICA

A247105 = Reap[Quiet @ For[n=1, n<28, n++, m = n; For[i=n, i >= 1, i--, For[j=1, j <= i, j++, t = Floor[(m*i)/(i-1)]; While[t - Floor[t/i] >= m, t -= 1];  om = m; m = t+1]]; Sow[om]]][[2, 1]] (* Jean-Fran├žois Alcover, Nov 28 2014, translated and adapted from Hiroaki Yamanouchi's Python script *)

PROG

(PARI) copydropmult(v, m)=vector(#v-#v\m, i, v[(i-1)*m\(m-1)+1])

alim(n)=my(r=vector(n, i, i), j=2, k=1); while(j<#r, r=copydropmult(r, j); if(k++>j, j++; k=1)); r

(Python)

for n in range(1, 101):

..m = n

..for i in range(n, 1, -1):

....for j in range(i):

......t = m * i // (i - 1)

......while t - t // i >= m:

........t -= 1

......m = t + 1

..print("%d %d" % (n, m)) # Hiroaki Yamanouchi, Nov 28 2014

CROSSREFS

Cf. A000960, A056533, A099204.

Sequence in context: A224129 A111641 A074419 * A272249 A275903 A273828

Adjacent sequences:  A247102 A247103 A247104 * A247106 A247107 A247108

KEYWORD

nonn

AUTHOR

Sergio Pimentel, Nov 18 2014

EXTENSIONS

More values from Franklin T. Adams-Watters, Nov 21 2014

a(12)-a(20) from Alois P. Heinz, Nov 26 2014

a(21)-a(27) from Hiroaki Yamanouchi, Nov 27 2014

STATUS

approved

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Last modified May 14 13:20 EDT 2021. Contains 343884 sequences. (Running on oeis4.)