Douglas Adams fans, prepare for a shock so big it'll knock you over and so interesting/engrossing you'll forget to hit the ground:

The answer to life, the universe and everything isn't the numerical value forty-two, but rather the digits 42, which, in every numerical base for which they are valid, represent a multiple of two which is not a multiple of four. Or put another way, those digits ALWAYS represent a multiple of two which is NEVER a multiple of any power of two, starting with base 5( the ordinally-primate base to have a digit representing the value four), in which 42 denotes 4 fives( equal to twenty) and 2 ones, for a minimum value of 22. Counting up or down by fours from there shows us the pattern that explains why 42 is such an important digit combination:

In base 2, binary, the value 6 is written 110( 1 four, 1 two, and 0 ones) and 10 is represented as 1010( 1 eight, 0 fours, 1 two, and 0 ones).

In base 3, 14 is 112( 1 nine, 1 three, 2 ones).

In base 4, 18 is 102.

In base 5, 22 is 42.

In base 6, 26 is 42.

In base 7, 30 is 42.

In base 8, 34 is 42.

In base 9, 38 is 42.

In base 10, 42 is 42.

In base 13, 54( "What do you get when you multiply 6 times 9?") is 42.

And so on...

Essentially, when seen this way, the series represents a new type of interesting number( multiples of two that AREN'T multiples of any power of two) which are much more predictable but equally as infinite and potentially as important as the primes, especially in geometry and computing; and maybe also in the identification of mathematical structures that constitute rings.

Because the prime factors of each of these numbers include only a single 2, and all non-quantum computing is binary, they might be useful in computing, either for the blockchain or security encryption, as they're essentially binary incompressible beyond that initial halving.

I hereby propose calling the series Adams's Numbers, a name which doesn't seem to be taken( not to be confused with Addams's Numbers.)( If it is taken, call 'em Serkey's Numbers. 😜)[ Or just say Douglas Adams's explicitly.]

And here's a proof I wrote for one interesting correlation within the series, that when you double a prime you get an Adams's number( although not all half-Adams's numbers are primes, obviously):

For n ≥ 1, 4n ± 2 is the formula identifying and defining the series "[Douglas ]Adams's Numbers", the nth member of which can be written as "42" in base_n, provided n ≥ 5.

Let 'p' represent any prime number greater than 2.

Let p - 1 = 2n

2p - 2 = 4n

2p = 4n + 2

so in any baseₙ, where n ≥ 5, 2p will be expressed as “42”. Next:

Let p + 1 = 2n

2p + 2 = 4n

2p = 4n - 2

ergo:

Let p ± 1 = 2n

2p ± 2 = 4n

2p = 4n ± 2

The double of any odd prime is an Adams's Number.