0,3

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

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.

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

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

Adjacent sequences: A014290 A014291 A014292 this_sequence A014294 A014295 A014296

Sequence in context: A036950 A127890 A127859 this_sequence A112700 A098105 A113034

nonn,easy,nice

Russ Cox (rsc(AT)swtch.com)

Additional links supplied by Lekraj Beedassy.