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.

1, 4, 10, 18, 30, 42, 58, 78, 102, 118, 150, 174, 210, 240, 274, 322, 360, 402, 442, 498, 540, 612, 648, 718, 780, 840, 918, 990, 1054, 1122, 1200, 1278, 1392, 1428, 1548, 1632, 1714, 1834, 1882, 2040, 2118, 2242, 2314, 2434, 2580, 2662, 2760, 2922, 3054

Offset: 1

Author

Paul D. Hanna, Oct 10 2005

Keywords

• nonn

Examples

			To get 10th term: 10->36->56->70->84->95->104->111->116->118.
To get 5th term: 5->16->24->28->30; since a(5) = A002491(9), compare with process used by A002491:
A002491(9) = 9->16->21->24->25->28->30->30->30.
		

Links

• Index entries for sequences related to the Josephus Problem

Crossrefs

Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.

Programs

Mathematica

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 *)

PARI

a(n)=local(A=n,D);for(i=1,n-1,D=n-i;A=D*ceil(A/D+2));A

Formula

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).