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Search: id:A002491
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| A002491 |
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Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of n-th hole.
(Formerly M1009 N0377)
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+0
24
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| 1, 2, 4, 6, 10, 12, 18, 22, 30, 34, 42, 48, 58, 60, 78, 82, 102, 108, 118, 132, 150, 154, 174, 192, 210, 214, 240, 258, 274, 282, 322, 330, 360, 372, 402, 418, 442, 454, 498, 510, 540, 570, 612, 622, 648, 672, 718, 732, 780, 802, 840, 870, 918
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A130747(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 23 2009]
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REFERENCES
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D. Betten, Kalahari and the Sequence "Sloane No. 377", Annals Discrete Math., 37, 51-58, 1988.
Y. David, On a sequence generated by a sieving process, Riveon Lematematika, 11 (1957), 26-31.
P. Erdos and E. Jabotinsky, On a sequence of integers ..., Indagationes Math., 20, 115-128, 1958.
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.4.7.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
K. S. Brown, Rounding Up To PI
D. M. Broline and D. E. Loeb (daniel.loeb(AT)verizon.net), The combinatorics of Mancala-Type games: Ayo, Tchoukaillon and 1/Pi, J. Undergrad. Math. Applic., vol. 16 (1995), pp. 21-36.
Nick Hobson, Python program for this sequence
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).
Index entries for sequences generated by sieves
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FORMULA
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To get n-th term, start with n and successively round up to next multiple of n-1, n-2, ..., 1.
Generated by a sieve: start with [ 1..n ]; keep first number, drop every 2nd, keep first, drop every 3rd, keep first, drop every 4th, etc.
Equals A007952(n)+1 or equally A108696(n)-1.
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EXAMPLE
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To get 10th term: 10->18->24->28->30->30->32->33->34->34.
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MATHEMATICA
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f[n_] := Fold[ #2*Ceiling[ #1/#2 + 0] &, n, Reverse@Range[n - 1]]; Array[f, 56] (from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 05 2005)
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CROSSREFS
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Cf. A028920, A028931, A028932, A028933.
Cf. A000012, A002491, A000960, A112557, A112558, A113742, A113743, A113744, A113745, A113746, A113747, A113748; A113749.
Sequence in context: A092249 A002088 A019332 this_sequence A045958 A076067 A065385
Adjacent sequences: A002488 A002489 A002490 this_sequence A002492 A002493 A002494
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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