



1, 1, 7, 79, 1021, 15621, 279931, 5764795, 134217721, 3486784393, 99999999991, 3138428376711, 106993205379061, 3937376385699277, 155568095557812211, 6568408355712890611, 295147905179352825841, 14063084452067724990993
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OFFSET

0,3


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 > (C1)(11/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 n1 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, Jun 04 2002


REFERENCES

H. E. Dudeney, The Canterbury Puzzles, Prob. 114 pp. 160161, 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.


LINKS

T. D. Noe, Table of n, a(n) for n=0..100
Anonymous, The Coconut Puzzle
J. Burkardt, The Coconut puzzle
Santo D'Agostino, “The Coconut Problem”; Updated With Solution, May 2011.
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 [Broken link?]
K. Uhland, Marx Brothers, Four Years Later [Broken link?]
Eric Weisstein's World of Mathematics, Monkey and Coconut Problem


FORMULA

E.g.f.: e^x(1x) + T/(1T)^3, where T=T(x) is Euler's tree function (see A000169).  Len Smiley Dec 10 2001


MATHEMATICA

Table[n^(n+1)n+1, {n, 0, 30}] (* Harvey P. Dale, Mar 24 2011 *)


CROSSREFS

Sequence in context: A127890 A198973 A127859 * A176792 A186377 A112700
Adjacent sequences: A014290 A014291 A014292 * A014294 A014295 A014296


KEYWORD

nonn,easy,nice


AUTHOR

Russ Cox


EXTENSIONS

Additional links supplied by Lekraj Beedassy.


STATUS

approved



