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%I A014293 #42 Sep 29 2023 03:55:56
%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 a(n) = n^(n+1) - n + 1.
%C A014293 Solution to the classic "Monkey and Coconut Problem" for n sailors.
%C A014293 Also called "Sailors and Monkey Problem": a(n) is smallest number such that C -> (C-1)*(1-1/n) can be applied 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 geometric progression 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_, 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="/A014293/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://web.archive.org/web/20120626221916/http://orion.math.iastate.edu/burkardt/puzzles/coconut_puzzle.html">The Coconut puzzle</a>.
%H A014293 Santo D'Agostino, <a href="https://qedinsight.wordpress.com/2011/05/13/the-coconut-problem/">"The Coconut Problem"; Updated With Solution</a>, May 2011.
%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="https://web.archive.org/web/20040423074548/http://uhlandkf.homestead.com/files/PuzzlePage/199412Pzl.htm">Marx Brothers, Four Years Later</a>.
%H A014293 K. Uhland, <a href="https://web.archive.org/web/20041124063822/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">Monkey and Coconut Problem</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_ Dec 10 2001
%t A014293 Table[n^(n+1)-n+1,{n,0,30}]  (* _Harvey P. Dale_, Mar 24 2011 *)
%K A014293 nonn,easy,nice
%O A014293 0,3
%A A014293 _Russ Cox_
%E A014293 Additional links supplied by _Lekraj Beedassy_

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