%I M2792 #47 Aug 07 2022 12:58:31
%S 1,3,9,25,57,145,337,793,1921,3849,8835,18889,41473,92305,203211,
%T 432699,944313,2027529,4077769,8745153,18133305,37898113,80713737,
%U 169730259,358760457,750591867,1575313473,3255787851,6751959507,14108682265,29364255033,61173205587
%N Multilevel sieve: at k-th step, accept k numbers, reject k, accept k, ...
%C Start with the natural numbers. For k=1,2,3,... successively do the following: accept k numbers, reject k numbers, accept k numbers, repeat indefinitely.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H N. J. A. Sloane, <a href="/A005209/b005209.txt">Table of n, a(n) for n = 1..1000</a> [Computed using Tom Duff's bc program]
%H Popular Computing (Calabasas, CA), <a href="/A005209/a005209.pdf">Contest 7 Results (based on solution from Tom Duff and Hugh Redelmeier)</a>, Vol. 4 (No. 43, Oct 1976), pp. 14-16. [Annotated scanned copy]
%H Jeffrey Shallit, <a href="/A001787/a001787.pdf">Letter to N. J. A. Sloane Mar 14, 1979, concerning A001787, A005209, A005210, A005211</a>
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%o (bc)
%o for(k=1;k<=100;k++){
%o n=k;
%o for(i=k-1;i>=1;--i) n=2*n-((n-1)%i)-1;
%o print k, " ", n, "\n"
%o } /* _Tom Duff_, Apr 24 2015 */
%o (Python)
%o from itertools import count, islice
%o def agen(): # generator of terms
%o for k in count(1):
%o n = k
%o for i in range(k-1, 0, -1): n = 2*n-((n-1)%i)-1
%o yield n
%o print(list(islice(agen(), 32))) # _Michael S. Branicky_, Aug 06 2022 after _Tom Duff_
%K nonn
%O 1,2
%A _N. J. A. Sloane_