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A014293
a(n) = n^(n+1) - n + 1.
7
1, 1, 7, 79, 1021, 15621, 279931, 5764795, 134217721, 3486784393, 99999999991, 3138428376711, 106993205379061, 3937376385699277, 155568095557812211, 6568408355712890611, 295147905179352825841, 14063084452067724990993
OFFSET
0,3
COMMENTS
Solution to the classic "Monkey and Coconut Problem" for n sailors.
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).
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
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.
LINKS
Anonymous, The Coconut Puzzle.
J. Burkardt, The Coconut puzzle.
R. V. Gassel et al., Coconut Chaos.
Eric Weisstein's World of Mathematics, Monkey and Coconut Problem.
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 Dec 10 2001
MATHEMATICA
Table[n^(n+1)-n+1, {n, 0, 30}] (* Harvey P. Dale, Mar 24 2011 *)
CROSSREFS
Sequence in context: A198973 A127859 A372969 * A176792 A186377 A112700
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Additional links supplied by Lekraj Beedassy
STATUS
approved