The Lost Numbers: 4 8 15 16 23 42

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.

Summary

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:

4=22
8=23
15=3*5
16=24
23=23 (prime)
42=2*3*7
108=22*33
741880=210*32*5*7*23

For reference:

  1. A prime number is a natural number, greater than 1, that is only divisible with itself and one.
  2. 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?

No, at least not in the first 3 200 000 000 digits, according to pisearch.
The decimal expansion of π is sequence A000796 in Sloane.

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.

For reference: Here is a Google search for Shaw-Basho polynomial.

(C) Marcus Dicander 2005-03-04
Last revision 2006-10-03
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Links

Mathworld - The best general mathematics resource.
Sloane - The best integer sequence resource.
Insultingly stupid movie physics - High quality commentary on science in movies.
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