| Questions like these make no sense. For every number you can think of, i can make a logic equation that will say it's a "logical" next number.
To make an example easy, let's look at sequence 1, 2, 3.
You can say the next number is 4, because you're counting 1,2,3,4...you can also say the next number is 5 and after that 8, because 1+2=3, 2+3=5, 3+5=8.
But you can also say the next number is 40.
Why? If you look at the function
p(x) = -24 + 78 x - (187x^2)/2 + (107x^3)/2 - (29x^4)/2 + (3x^5)/2
and calculate p(1) you will get 1.
p(2)=2
p(3)=3
p(4)=40
But you can also say 70!
Why?
Take a look at h(x) = -54 + 169x - (397x^2)/2 + 111x^3 - (59x^4)/2 + 3x^5
h(1)=1
h(2)=2
h(3)=3
h(4)=70
Basically, for any given number, you can find a "logic" for just THAT number to be the next in line.
Lets say you want to prove you can find a logic for PI to be the next number in sequence.
Just take a look at function
g(x) = 4 - PI - (19*x)/3 + (11*PI*x)/6 + 4x^2 - PI*x^2 - (2x^3)/3 + (PI*x^3)/6
g(1)=1
g(2)=2
g(3)=3
g(4)=PI |