OFFSET
1,2
COMMENTS
This is a generalization (from n = 5) of Ben Ames Williams's published problem. For a given n, the problem is effectively as follows. A successful monkey-share process removes 1 coconut for a monkey followed by an exact share of 1/n from the coconut pile. Determine the least initial number of coconuts for a monkey-share to succeed n times, leaving a multiple of n to be shared equally at the end. The problem in the D'Agostino link is slightly different, requiring a coconut for the monkey in the final division. - Peter Munn, Jun 14 2023
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..100
Anonymous, The Monkey and the Coconuts (with FormulaOne program)
Santo D'Agostino, “The Coconut Problem”; Updated With Solution, May 2011.
Mark Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Famous Coconuts Problem, The Winnower, Authorea (2016) Vol. 3.
R. S. Underwood and Robert E. Moritz, Problem 3242, Amer. Math. Monthly, 35 (1928), 47-48.
Robert G. Wilson v, Letter to N. J. A. Sloane, Oct. 1993
FORMULA
E.g.f.: (1-x)*exp(x)-(W(x)+2)*(2*W(x)+1)/(2*(1+W(x))^3)-W(-x)/(2*(1+W(-x))^3) where W is the Lambert W function. - Robert Israel, Aug 26 2016
a(n) = 1-n-(-n)^n+(1+(-1)^n)*n^(n+1)/2. - Wesley Ivan Hurt, Nov 09 2023
MAPLE
seq(`if`(n::even, (n-1)*(n^n - 1), n^n-n+1), n=1..30); # Robert Israel, Aug 26 2016
MATHEMATICA
Table[If[EvenQ[n], (n-1)(n^n-1), n^n-n+1], {n, 30}] (* Harvey P. Dale, Apr 21 2012 *)
PROG
(Python)
def a(n): return (n-1)*(n**n - 1) if n%2 == 0 else n**n - n + 1
print([a(n) for n in range(1, 20)]) # Michael S. Branicky, Feb 07 2022
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Apr 21 2012
STATUS
approved