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

1,2

Links

Table of n, a(n) for n=1..49.

Index entries for sequences related to the Josephus Problem

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).

Example

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.

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

Prog

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

Crossrefs

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

Sequence in context: A025712 A283969 A022781 * A332490 A008246 A301284

Adjacent sequences: A112554 A112555 A112556 * A112558 A112559 A112560

Keyword

nonn

Author

Paul D. Hanna, Oct 10 2005

Status

approved