

A094062


a(n) = ceiling((3sqrt(3))*4^(n3)) + 1 for n>=2, a(1)=1.


1



1, 2, 3, 7, 22, 83, 326, 1300, 5195, 20776, 83098, 332387, 1329543, 5318166, 21272659, 85090631, 340362521, 1361450080, 5445800316, 21783201259, 87132805033, 348531220128, 1394124880509, 5576499522030, 22305998088117
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 CamelBanana Problem, Nieuw Archief voor de Wiskunde, 144, No. 3, 1996, pp. 415426.
Matthijs Coster, Camels and Bananas, Preprint, Apr 29, 2004


LINKS



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((3sqrt(3))*4^(n3)) + 1); /* Joerg Arndt, Oct 20 2012 */


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



