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1, 1, 7, 79, 1021, 15621, 279931, 5764795, 134217721, 3486784393, 99999999991, 3138428376711, 106993205379061, 3937376385699277, 155568095557812211, 6568408355712890611, 295147905179352825841, 14063084452067724990993
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Solution to the classical "Monkey and Coconut Problem" for n sailors.
Also called "Sailors and Monkey Problem": a(n) is smallest number such that can apply C -> (C-1)(1-1/n) n times and at every step have an integer C = 1 mod n.
The expression for a(n) is easily derived from the observation that had an extra n-1 coconuts been added to the original pile a(n), the monkey would have been doomed to a zero coconut tip all through, the successive heaps of leftovers then collapsing to an ordinary G.P. of common ratio (1 - 1/n). For a total number of (n+1) interventions, we thus have n^(n+1) dividing a(n) + (n - 1), whence the formula. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 04 2002
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REFERENCES
| H. E. Dudeney, The Canterbury Puzzles, Prob. 114 pp. 160-161, 250, Nelson, London 1919.
M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles & Diversions, p. 108, Simon & Shuster, NY 1961.
P. Halmos, Problems for Mathematicians Young and Old, MAA DC 1991.
W. L. Schaff, A Bibliography of Recreational Mathematics, Vol. 2 Chap. 1.18c, p. 24, NCTM Washington D. C., 1970.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
Anonymous, The Coconut Puzzle
J. Burkardt, The Coconut puzzle
R. V. Gassel et al., Coconut Chaos
MathKnox, Puzzle of the week
J. S. Tanton, A collection of research problems
K. Uhland, Marx Brothers, Four Years Later
K. Uhland, Marx Brothers, Four Years Later
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
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FORMULA
| E.g.f.: e^x(1-x) + T/(1-T)^3, where T=T(x) is Euler's tree function (see A000169). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 10 2001
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MATHEMATICA
| Table[n^(n+1)-n+1, {n, 0, 30}] (* From Harvey P. Dale, Mar 24 2011 *)
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CROSSREFS
| Sequence in context: A127890 A198973 A127859 * A176792 A186377 A112700
Adjacent sequences: A014290 A014291 A014292 * A014294 A014295 A014296
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Russ Cox (rsc(AT)swtch.com)
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EXTENSIONS
| Additional links supplied by Lekraj Beedassy.
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