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Discovering the Hidden Sequence in 1 Divided by 998001
A Mathematical Journey
In the realm of mathematics, certain numbers and operations hold secrets waiting to be unveiled. One such curiosity lies in the division of 1 by 998001. This division is not just a simple arithmetic operation but a gateway to a fascinating pattern that intrigues mathematicians and enthusiasts alike. Upon diving deep into this calculation, one discovers that it yields all three-digit numbers from 000 to 999 in order, with the notable exception of 998. This article explores this phenomenon and delves into the analysis of why 998 is conspicuously absent from this sequence.
The Calculation
When 1 is divided by 998001, the quotient is a decimal that extends far beyond the standard precision most are accustomed to. To fully appreciate the pattern, one must calculate the division to at least 2000 decimal places. With the aid of arbitrary precision arithmetic facilitated by computational tools, it’s possible to observe the entire sequence unfold.
# To accurately calculate 2000 digits of 1 divided by 998001, we can use the Decimal module which allows for arbitrary precision arithmetic.
from decimal import Decimal, getcontext
# Set the precision to 2000 digits after the decimal point
getcontext().prec = 2002 # 2 extra digits for the…
