A239341 Decimal expansion of 7 + 2021/3003.

7, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7, 2, 9, 9, 3, 6, 7

Offset

1,1

Comments

7, then repeat 6,7,2,9,9,3.

A motorcycle whose fuel tank has a capacity of 1 unit of fuel can travel halfway across a desert on one full tank of fuel, and it can establish its own refueling stations at any locations along the way. At any refueling station, fuel can be transferred from the motorcycle's fuel tank to or from storage at the refueling station. The rider of the motorcycle has an unlimited supply of fuel at the starting point. No fuel can be carried by the motorcycle other than the fuel in its fuel tank. The constant can be interpreted as the minimum total number of tankfuls of fuel needed to cross the desert.

Let x be the distance that the motorcycle can travel given one tankful of fuel; the width of the desert is then 2*x. The maximum desert width that can be crossed given y tankfuls of fuel is f(y) = (1 + 1/3 + 1/5 + ... + 1/(2*k-1) + (y-k)/(2*k + 1))*x where k = floor(y). Since f(7) < 2*x < f(8), crossing a desert of width 2*x requires y tankfuls of fuel where floor(y) = 7. Solving (1 + 1/3 + 1/5 + ... + 1/(2*7-1) + (y-7)/(2*7 + 1))*x = 2*x for y gives y = 7 + 15*(2 - (1 + 1/3 + 1/5 + ... + 1/13)) = 23042/3003 = 7.672993672993... - Jon E. Schoenfield, Feb 27 2020

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Jeep Problem

Wikipedia, Jeep problem

Example

7.672993672993672993672993672993672993672993672993672993672993672993672...

Mathematica

Join[{7}, Flatten[Table[{6, 7, 2, 9, 9, 3}, {17}]]]
Join[{7}, PadRight[{}, 104, {6, 7, 2, 9, 9, 3}]]

Prog

(Magma) [7] cat &cat[[6, 7, 2, 9, 9, 3]: n in [1..17]];

Crossrefs

Sequence in context: A247314 A257395 A197687 * A239606 A291423 A276792

Adjacent sequences: A239338 A239339 A239340 * A239342 A239343 A239344

Keyword

nonn,cons,easy

Author

Arkadiusz Wesolowski, Mar 16 2014

Extensions

Comments section edited by Jon E. Schoenfield, Feb 27 2020

Status

approved