A136120 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).
1, 3, 4, 5, 9, 10, 15, 16, 22, 23, 24, 25, 26, 36, 37, 48, 49, 50, 51, 52, 53, 69, 70, 87, 88, 89, 90, 91, 92, 93, 116, 117, 141, 142, 167, 168, 194, 195, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 269, 270, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317
Offset: 1
Examples
First few steps are: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,... n = 1, a(1) = 1; delete terms at positions 2 to 2; this is 2; 1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,... n = 2,a(2) = 3; delete terms at positions 5 to 7; these are 6,7,8; 1,3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,22,... n = 3, a(3) = 4; delete terms at positions 7 to 10; these are 11,12,13,14; 1,3,4,5,9,10,15,16,17,18,19,20,21,22,23,24,25,26,27,28,... n = 4, a(4) = 5; delete terms at positions 9 to 13; these are 17,18,19,20,21; 1,3,4,5,9,10,15,16,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36... n = 5 a(5) = 9; delete terms at positions 14 to 22; these are 27,28,29,30,31,32,33,34,35; 1,3,4,5,9,10,15,16,22,23,24,25,26,36,...
Links
- Klaus Brockhaus, Table of n, a(n) for n=1..10000
- D. X. Charles, Sieve Methods, July 2000, University of Wisconsin.
- Rémi Eismann, Decomposition into weight * level + jump and application to a new classification of primes, arXiv:0711.0865 [math.NT]
- M. C. Wunderlich, A general class of sieve generated sequences, Acta Arithmetica XVI,1969, pp.41-56.
- Index entries for sequences generated by sieves
Programs
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Mathematica
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 *)
Extensions
Edited and extended by Klaus Brockhaus, Apr 20 2008