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A112557 Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of (2*n-1)-th hole for n>=1; a bisection of A002491.

%I A112557 #17 Aug 12 2025 02:57:43
%S A112557 1,4,10,18,30,42,58,78,102,118,150,174,210,240,274,322,360,402,442,
%T A112557 498,540,612,648,718,780,840,918,990,1054,1122,1200,1278,1392,1428,
%U A112557 1548,1632,1714,1834,1882,2040,2118,2242,2314,2434,2580,2662,2760,2922,3054
%N A112557 Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of (2*n-1)-th hole for n>=1; a bisection of A002491.
%H A112557 <a href="/index/J#Josephus">Index entries for sequences related to the Josephus Problem</a>
%F A112557 To get n-th term, start with n and successively round up to next 3 multiples of n-1, n-2, ..., 1 (compare to method used by A002491). Surprisingly, a(n) = A002491(2*n-1).
%e A112557 To get 10th term: 10->36->56->70->84->95->104->111->116->118.
%e A112557 To get 5th term: 5->16->24->28->30; since a(5) = A002491(9), compare with process used by A002491:
%e A112557 A002491(9) = 9->16->21->24->25->28->30->30->30.
%t A112557 f[n_] := Fold[ #2 * Ceiling[ #1/#2 + 2] &, n, Reverse @ Range[n - 1]]; Array[ f, 49] (* Bobby R. Treat (drbob(at)bigfoot.com), Oct 11 2005 *)
%o A112557 (PARI) a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+2));A
%Y A112557 Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.
%K A112557 nonn
%O A112557 1,2
%A A112557 _Paul D. Hanna_, Oct 10 2005