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A014293
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a(n) = n^(n+1) - n + 1.
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7
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1, 1, 7, 79, 1021, 15621, 279931, 5764795, 134217721, 3486784393, 99999999991, 3138428376711, 106993205379061, 3937376385699277, 155568095557812211, 6568408355712890611, 295147905179352825841, 14063084452067724990993
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OFFSET
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0,3
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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FORMULA
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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
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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