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Search: id:A112557
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| A112557 |
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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. |
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12
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| 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
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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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).
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EXAMPLE
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To get 10-th term: 10->36->56->70->84->95->104->111->116->118.
To get 5-th 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.
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MATHEMATICA
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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
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PROGRAM
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(PARI) a(n)=local(A=n, D); for(i=1, n-1, D=n-i; A=D*ceil(A/D+2)); A
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CROSSREFS
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Cf. A000012, A002491, A000960 (Flavius Josephus's sieve), A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.
Sequence in context: A009880 A025712 A022781 this_sequence A008246 A024983 A009896
Adjacent sequences: A112554 A112555 A112556 this_sequence A112558 A112559 A112560
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 10 2005
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