Yes, this is a math thread. YOU HAVE BEEN WARNED. And there are religious aspects as well.
A Hitchhiker’s Guide to the Number 42
In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins.
Ancient Tibet had 42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.
The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”
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.
Mathematically Unique?
The number 42 has a range of interesting mathematical properties. Here are some of them:
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 corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), 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)(4n – 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.
The number 42 is the sum of the first two nonzero integer powers of six—that is, 61 + 62 = 42. The sequence b(n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. It is defined by the formulas b(0) = 0, b(n) = 6b(n – 1) + 6. The density of these numbers also tends toward zero at infinity.
Forty-two is a Catalan number.
Problem of the Sum of Three Cubes
What integers n can be written as the sum of three whole-number cubes (n = a3 + b3 + c3)?
The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed:
42 = (–80,538,738,812,075,974)3 + 80,435,758,145,817,5153 + 12,602,123,297,335,6313
A Hitchhiker’s Guide to the Number 42
In ancient Egyptian mythology, during the judgment of souls, the dead had to declare before 42 judges that they had not committed any of 42 sins.
Ancient Tibet had 42 rulers. Nyatri Tsenpo, who reigned around 127 B.C., was the first. And Langdarma, who ruled from 836 to 842 A.D. (i.e., the 42nd year of the ninth century), was the last.
The Gutenberg Bible, the first book printed in Europe, has 42 lines of text per column and is also called the “Forty-Two-Line Bible.”
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.
Mathematically Unique?
The number 42 has a range of interesting mathematical properties. Here are some of them:
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 corresponds to entry A020988 in The On-Line Encyclopedia of Integer Sequences (OEIS), 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)(4n – 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.
The number 42 is the sum of the first two nonzero integer powers of six—that is, 61 + 62 = 42. The sequence b(n), which is the sum of the powers of six, corresponds to entry A105281 in OEIS. It is defined by the formulas b(0) = 0, b(n) = 6b(n – 1) + 6. The density of these numbers also tends toward zero at infinity.
Forty-two is a Catalan number.
Problem of the Sum of Three Cubes
What integers n can be written as the sum of three whole-number cubes (n = a3 + b3 + c3)?
The answer came in a 2020 preprint, the result of a huge computational effort coordinated by Booker and Andrew Sutherland of the Massachusetts Institute of Technology. Computers participating in the Charity Engine network of personal computers, calculating for the equivalent of more than one million hours, showed:
42 = (–80,538,738,812,075,974)3 + 80,435,758,145,817,5153 + 12,602,123,297,335,6313
