%I #19 Feb 14 2015 12:39:34

%S 1,3,4,5,9,10,15,16,22,23,24,25,26,36,37,48,49,50,51,52,53,69,70,87,

%T 88,89,90,91,92,93,116,117,141,142,167,168,194,195,222,223,224,225,

%U 226,227,228,229,230,231,232,269,270,308,309,310,311,312,313,314,315,316,317

%N Limiting sequence when we start with the positive integers (A000027) and at step n >= 1 delete the a(n) terms at positions n+a(n) to n-1+2*a(n).

%H Klaus Brockhaus, <a href="/A136120/b136120.txt">Table of n, a(n) for n=1..10000</a>

%H D. X. Charles, <a href="http://pages.cs.wisc.edu/~cdx/Sieve.pdf">Sieve Methods</a>, July 2000, University of Wisconsin.

%H Rémi Eismann, <a href="http://arXiv.org/abs/0711.0865">Decomposition into weight * level + jump and application to a new classification of primes</a>, arXiv:0711.0865 [math.NT]

%H M. C. Wunderlich, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1614.pdf">A general class of sieve generated sequences</a>, Acta Arithmetica XVI,1969, pp.41-56.

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%e First few steps are:

%e 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,...

%e n = 1, a(1) = 1; delete terms at positions 2 to 2; this is 2;

%e 1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,...

%e n = 2,a(2) = 3; delete terms at positions 5 to 7; these are 6,7,8;

%e 1,3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,22,...

%e n = 3, a(3) = 4; delete terms at positions 7 to 10; these are 11,12,13,14;

%e 1,3,4,5,9,10,15,16,17,18,19,20,21,22,23,24,25,26,27,28,...

%e n = 4, a(4) = 5; delete terms at positions 9 to 13; these are 17,18,19,20,21;

%e 1,3,4,5,9,10,15,16,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36...

%e n = 5 a(5) = 9; delete terms at positions 14 to 22; these are 27,28,29,30,31,32,33,34,35;

%e 1,3,4,5,9,10,15,16,22,23,24,25,26,36,...

%t f[seq_] := Module[{s = seq, n1, n2}, n++; n1 = s[[n]] + n; If[n1 <= len, n2 = Min[n - 1 + 2*s[[n]], len]; len -= n2 - n1 + 1; Drop[s, {n1, n2}], s]]; n = 0; len = 1000; FixedPoint[f, Range[len]] (* _Jean-François Alcover_, Sep 29 2011 *)

%Y Cf. A000027, A139418, A139419, A139420, A136110, A136119, A137292.

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, Mar 16 2008

%E Edited and extended by _Klaus Brockhaus_, Apr 20 2008