A005209 - OEIS

%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_