The numbers 4, 8, 15, 16, 23 and 42 are one of TV series Lost’s most prominent recurring themes.

It has been revealed in The Lost Experience that these six numbers are the core values of the Valenzetti Equation, a mathematical formula designed to predict the end of humanity. The numbers in actuality are said to represent human and environmental factors in the equation (given numerical form). One purpose of the DHARMA Initiative was to change the factors leading to humanity’s demise, which will be indicated by an alteration in at least one of the human/environmental factors – i.e. the numbers. However, in all its years of research, the Initiative failed to reach its goal. Despite much research and manipulation of the equation’s values, the end result was always the numbers.

There are endless equations producing the Six Numbers series.

The sixth grade equation

Here is a sixth grade equation with numbers 4, 8, 15, 16, 23 and 42 as solution:

x⁶ – 108x⁵ + 4405x⁴ – 87270x³ + 881464x² -4239552x + 7418880 = 0

Mikau’s expression with inputs from 1 to 6

Mikau proposed here a mathematical expression which, for values of n between 1 and 6, produced the series 4, 8, 15, 16, 23, 42:

60 – 122,4n + 91,75n² -29,375n³ + 4,25n⁴ – 0,225n⁵

Shaw-Basho Series

The Six Numbers can be also found in the Shaw-Basho Series: by defining the series A_0,n as:

A_0,n = (42n⁵ – 305n⁴ + 1100n³ – 895n² + 1018n + 480) / 120

and a second series A_1,n as:

A_1,n = A_0,n+1 – A_0,n

the procedure can be generalised by defining a class of series like this:

A_m,n = A_m-1,n+1 – A_m-1,n

Given these definitions, the series A_m,1 starts with the Six Numbers, followed by all zeros:

A_m,1 = { 4, 8, 15, 16, 23, 42, 0, 0, 0... }

The recursive series

Another series containing the Six Numbers is the one which can be defined in a recursive way following this rule:

A_i = A_i-1 + A_i-3 + A_i-5

By choosing these first five elements:

A₁ = -3, A₂ = -1, A₃ = 4, A₄ = 8, A₅ = 15

the subseries A_3...8 is { 4, 8, 15, 16, 23, 42 }