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The number 42 has a wide range of interesting mathematical properties. Here are some of them which will totally bend your mind:
The number is the sum of the first three odd powers of two—that is, 21 + 23 + 25 = 42. It is an element in the sequence a(n), which is the sum of n odd powers of 2 for n > 0. The sequence created by mathematician Neil Sloane. In base 2, the nth element may be specified by repeating 10 n times (1010 ... 10). The formula for this sequence is a(n) = (2/3)(4 n – 1). As n increases, the density of numbers tends toward zero, which means that the numbers belonging to this list, including 42, are exceptionally rare.
Forty-two is a Catalan number. These numbers are extremely rare, much more so than prime numbers and also a practical number,which means that any integer between 1 and 42 is the sum of a subset of its distinct divisors.
An obvious question, which indeed has been asked, is whether the use of 42 in Adams’s books had any particular meaning for the author.In the binary system, or base 2, 42 is written as 101010, which is pretty simple an easy.The reference to base 13 in Adams’s answer requires a more indirect explanation. In one instance, the series suggests that 42 is the answer to the question “What do you get if you multiply six by nine?” That idea seems absurd because 6 x 9 = 54. But in base 13, the number expressed as “42” is equal to (4 x 13) + 2 = 54.
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-Charu Surana Editorial Team
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