OFFSET
1,2
COMMENTS
From a new version of the camel problem. The original camel problem is discussed by de Bondt. A camel can carry one banana at a time on his back. It is on a diet and therefore can only have one banana at a time in its stomach. As soon as it has eaten a banana it walks a mile and then needs a new banana (in order to be able to continue its itinerary).
Let there be a stock of N bananas at the border of the desert. How far can the camel penetrate into the desert? (Of course it can form new stocks with transported bananas.)
The new version: Find a(n), the number of bananas needed for the camel to penetrate into the desert at least n miles.
REFERENCES
Michiel de Bondt, The Camel-Banana Problem, Nieuw Archief voor de Wiskunde, 14-4, No. 3, 1996, pp. 415-426.
Matthijs Coster, Camels and Bananas, Preprint, Apr 29, 2004
LINKS
Michiel de Bondt, The Camel-Banana Problem, arXiv:2403.19667 [math.HO], 2024.
Matthijs Coster, Sequences
MATHEMATICA
With[{s = Sqrt[3]}, MapAt[# - 1 &, Array[Ceiling[(3 - s)*4^(# - 3)] + 1 &, 25], 1]] (* Michael De Vlieger, Dec 07 2020 *)
PROG
(PARI) a(n) = if(n<=1, n==1, ceil((3-sqrt(3))*4^(n-3)) + 1); /* Joerg Arndt, Oct 20 2012 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Matthijs Coster, Apr 29 2004
EXTENSIONS
More terms from Joshua Zucker, May 03 2006
STATUS
approved