In the TV-series “Lost”, Episode 18, the plot revolves around six numbers. This page deals with their mathematical significance (or lack thereof). This page does not deal with occurences of the numbers within the show, within other works of fiction or within other nonmathematical works of nonfiction, nor does it cover occult interpretations of their meaning. For pages that address those issues Google is your friend.
The Lost Numbers are not part of a longer integer sequence. There is no known pattern that is consistent and specific for The Lost Numbers.
Is this a known integer sequence?
Answer: No it isn’t. The most comprehensive list of integer sequences is Sloane and it is not listed there. [Update: Because of this page “The Lost Numbers” are now listed as sequence A104101. [In the TV-series “Alias”, the antagonist’s name is Sloane. This is a coincidence.]]
Are they prime numbers?
One of them, 23, is indeed a prime number. The others are not. For your convenience, here are the prime factorizations:
- A prime number is a natural number, greater than 1, that is only divisible with itself and one.
- Every number greater than 1 is either a prime or can be expressed as a product of primes.
The prime numbers are sequence A000040 in Sloane.
Are they perfect numbers?
No. The first perfect numbers are 6, 28 and 496. But there are 6 numbers so out of coincidence the number of numbers is a perfect number.
For reference: A perfect number is a number that is the same as the sum of its divisors (except itself) for example 6=1+2+3 and 28=1+2+4+7+14.
The perfect numbers are sequence A000396 in Sloane.
Are they decimals of π?
Can we leave out a number?
4, 8, 15, 16 and 23 are part of the two previously known sequences:
A084345, the numbers with non-prime number of 1:s in their binary expansion.
A084561, the numbers with square number of 1:s in their binary expansion.
For your convenience, here are all binary expansions (and their hex representation):
dec binary hex 4 = %0000100 = 0x04 8 = %0001000 = 0x08 15 = %0001111 = 0x0F 16 = %0010000 = 0x10 23 = %0010111 = 0x17 42 = %0101010 = 0x2A 108 = %1101100 = 0x6C 7418880 = %11100010011010000000000 = 0x713400
However, a mathematical property of The Lost Numbers would have to apply to all numbers and not just most of them. So this coincidence does not count either.
What is the Shaw-Basho polynomial?
It is a well chosen polynomial that together with a well chosen set of operations generates the Lost Numbers. It is not canonical Lost-content. It is not of mathematical significance. It is not endorsed by the author of this page. It is just a hoax.
- Use a search engine to look for Shaw-Basho polynomial. The hits will be the hoax page and some forum comments.
- Shaw and Basho are not famous mathematicians. Just the perpetrator and his cat. (Check his web page).
- Infinitely many Integer Sequences can be generated using the same technique and a well chosen polynomial.
For reference: Here is a Google search for Shaw-Basho polynomial.
The Jar labels: DI 9FFTR731
731 is a composite number (17*43) but 7331, 73331, 733331 and 7333331 are all prime. 731 is the only three-digit composite with this property. 137 (731 backwards) is prime and so are 13, 37, 73 and 31. See prime curious for more.
–> (C) Marcus Dicander 2005-03-04
Last revision 2006-10-03
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<a href=”http://www.d.kth.se/~dicander/lost.html”>The Lost Numbers – 4 8 15 16 23 42</a>