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%I #61 Sep 30 2022 07:50:11
%S 0,1,3,5,9,11,17,21,29,33,41,47,57,59,77,81,101,107,117,131,149,153,
%T 173,191,209,213,239,257,273,281,321,329,359,371,401,417,441,453,497,
%U 509,539,569,611,621,647,671,717,731,779,801,839,869,917,929,989,1001,1053,1067
%N Generated by a sieve: keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.
%C Also called the sieve of Tchoukaillon (or Mancala, or Kalahari).
%C If k+1 occurs at rank i for the first time, then i is given by the program: i = 0: for j = k to 1 step -1: i = 1 + i + int ( i / j ): next: - Claude Lenormand (claude.lenormand(AT)free.fr), Jan 15 2001
%C A082447(n+1) = (number of terms <= n); see A141262 for primes. - _Reinhard Zumkeller_, Jun 21 2008
%D Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.
%D M. Le, On the Smarandache n-ary Sieve, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 146-147.
%H L. K. Mitchell, <a href="/A007952/b007952.txt">Table of n, a(n) for n = 0..7549</a>
%H D. Betten, <a href="https://doi.org/10.1016/S0167-5060(08)70224-3">Kalahari and the Sequence "Sloane No. 377"</a>, Annals Discrete Math., 37, 51-58, 1988.
%H D. M. Broline and Daniel E. Loeb, <a href="https://arxiv.org/abs/math/9502225">The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi</a>, arXiv:math/9502225 [math.CO], 1995; J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.
%H P. Erdős and E. Jabotinsky, On a sequence of integers ..., Indagationes Math., 20, 115-128, 1958. <a href="http://www.renyi.hu/~p_erdos/1958-08.pdf">part I</a> <a href="http://www.renyi.hu/~p_erdos/1958-09.pdf">part II</a>
%H N. J. A. Sloane, <a href="http://neilsloane.com/doc/sg.txt">My favorite integer sequences</a>, in Sequences and their Applications (Proceedings of SETA '98).
%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>
%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>
%F Equals A002491(n) - 1. Equals A108696 - 2.
%t f[n_] := Fold[#2*Floor[#1/#2 + 1] &, n, Reverse@ Range[n - 1]]; Array[f, 55] (* From David Wilson *)
%o (Haskell)
%o a007952 n = a007952_list !! n
%o a007952_list = f 1 [0..] where
%o f k (x:xs) = x : f (k + 1) (g xs) where
%o g ws = us ++ (g vs) where (us, _:vs) = splitAt k ws
%o -- _Reinhard Zumkeller_, Jan 19 2014
%o (PARI) a(n) = my(ret=0); forstep(k=n,1,-1, ret++; ret+=(-ret)%k); ret; \\ _Kevin Ryde_, Sep 30 2022
%Y Cf. A002491, A028920, A028931, A028932, A028933, A108696, A140060, A141271, A141272.
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_, R. Muller
%E Corrected and extended by _David W. Wilson_
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