A094062 a(n) = ceiling((3-sqrt(3))*4^(n-3)) + 1 for n>=2, a(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

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

Table of n, a(n) for n=1..25.

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

Sequence in context: A053966 A010738 A114599 * A038159 A077210 A324620

Adjacent sequences: A094059 A094060 A094061 * A094063 A094064 A094065

Keyword

nonn,easy

Author

Matthijs Coster, Apr 29 2004

Extensions

More terms from Joshua Zucker, May 03 2006

Status

approved