Search: id:A014293
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%I A014293
%S A014293 1,1,7,79,1021,15621,279931,5764795,134217721,3486784393,99999999991,
%T A014293 3138428376711,106993205379061,3937376385699277,155568095557812211,
%U A014293 6568408355712890611,295147905179352825841,14063084452067724990993
%N A014293 n^(n+1)-n+1.
%C A014293 Solution to the classical "Monkey and Coconut Problem" for n sailors.
%C A014293 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.
%C A014293 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
%D A014293 H. E. Dudeney, The Canterbury Puzzles, Prob. 114 pp. 160-161, 250, Nelson, 
               London 1919.
%D A014293 M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles 
               & Diversions, p. 108, Simon & Shuster, NY 1961.
%D A014293 P. Halmos, Problems for Mathematicians Young and Old, MAA DC 1991.
%D A014293 W. L. Schaff, A Bibliography of Recreational Mathematics, Vol. 2 Chap. 
               1.18c, p. 24, NCTM Washington D. C., 1970.
%H A014293 T. D. Noe, <a href="b014293.txt">Table of n, a(n) for n=0..100</a>
%H A014293 Anonymous, <a href="http://www.tickey.co.za/maths/Puzzles%20-%20%20Coconut%20puzzle.pdf">
               The Coconut Puzzle</a>
%H A014293 J. Burkardt, <a href="http://orion.math.iastate.edu/burkardt/puzzles/
               coconut_puzzle.html">The Coconut puzzle</a>
%H A014293 R. V. Gassel et al., <a href="http://puzzle.dse.nl/teasers/index_us.html#coconut_chaos">
               Coconut Chaos</a>
%H A014293 MathKnox, <a href="http://math.knox.edu/puzzles/Catalog-Old/jan25tofeb1_2000.html">
               Puzzle of the week</a>
%H A014293 J. S. Tanton, <a href="http://www.themathcircle.org/researchproblems.php">
               A collection of research problems</a>
%H A014293 K. Uhland, <a href="http://uhlandkf.homestead.com/files/PuzzlePage/199412Pzl.htm#Return2">
               Marx Brothers, Four Years Later</a>
%H A014293 K. Uhland, <a href="http://uhlandkf.homestead.com/files/PuzzlePage/199412Sol.htm">
               Marx Brothers, Four Years Later</a>
%H A014293 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MonkeyandCoconutProblem.html">Link to a section of The World of Mathematics</
               a>
%F A014293 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
%Y A014293 Sequence in context: A036950 A127890 A127859 this_sequence A112700 A098105 
               A159524
%Y A014293 Adjacent sequences: A014290 A014291 A014292 this_sequence A014294 A014295 
               A014296
%K A014293 nonn,easy,nice
%O A014293 0,3
%A A014293 Russ Cox (rsc(AT)swtch.com)
%E A014293 Additional links supplied by Lekraj Beedassy.

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