

A239341


Decimal expansion of 7 + 2021/3003.


0



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
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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*k1) + (yk)/(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*71) + (y7)/(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



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



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



