All sequence riddles are wrong .why?

[DavidWhitbeck]

You don't even have to do fit to a polynomial fit, sequences do not have to have rules, so the next term in the sequence can be whatever you want it to be.

 

[CRGreathouse]

You don't even have to do fit to a polynomial fit, sequences do not have to have rules, so the next term in the sequence can be whatever you want it to be.

Fair point. So the next member of "1, 2, 4, 8, 16, 32" could be "dragon".

 

[Dragonfall]

Here's an idea for a sequence riddle: given a countable sequence of natural numbers, what ordinals come next?

Say N=(1, 2, 3, 4, ...), I could say what comes next are all ordinals. OR I could say that what comes next are all SINGULAR ordinals, etc.

 

[mubashirmansoor]

Thats good!

Very interesting thread...

I have had some research (not a serious one) on the polynomial sequences when I was in high school. I know this is not exactly what you are looking for but this is what you might find interesting.

I found a single function definition which would do all the work you have been doing in post#1,

I have attached the function to the post as a jpg.

n represents the degree of the polynomial
delta "x" can be anything
"C" represents combinations.

______

comments will be highly appreciated

 

[DavidWhitbeck]

Fair point. So the next member of "1, 2, 4, 8, 16, 32" could be "dragon".

No because sequences are by definition subsets of N.

 

[lurflurf]

No because sequences are by definition subsets of N.

Those are natual number sequences

There are real sequences like
3,3.1,3.14,3.1415,3.1415926,3.141592653...
rational seqences
.1,.11,.111,.1111,.11111,...

A sequence is a mapping of the natural numbers to an arbitrary set
or if one prefers
we can define a seed and a map f:S->S
ie
seed=a0
a1=f(a0)
sucsessor(an)=an+1
f^n(seed)=an

 

[lurflurf]

All this said there is some value in trying to choose a best in some sense sucsession function given a run of a sequence
thhe trouble is knowing which sense our some sense should be

 

[lurflurf]

A sequence is a mapping of the natural numbers to an arbitrary set
or if one prefers
we can define a seed and a map f:S->S

Oops not general enough
we will just go with
f:N->S
S an arbitrary set
so maybe we have

1,2,3,4,5,...,88,89,pickles

 

[Diffy]

A sequence is a mapping of the natural numbers to an arbitrary set
n

I may just be playing devil's advocate, but who says sequences have to be infinite?

1, 3, 4, 6, 8 ...

what comes next? perhaps the answer is undefined, or nothing.

 

[lurflurf]

good point there are I speak of one popular sequence there are also
finite sequences
double sequences
sequences over other index sets like
Moore-Smith sequences

many times the tradition sequence structure can be used
such as
11/8,9/7,7/6,5/5,3/4,1/3,-1/2,-3/1,-5/0,-7/-1
we could interpet formally, or if it is to be interpeted as division well could mark problems as "undefind" which we could ad to the domain

for finite sets we could repeat the final entry of append a sybmol
1,2,3,4,5
could be
1,2,3,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,...
0r
1,2,3,4,5,0,0,0,0,0,0,0,0,0,0,0,0,0,0,...
or
1,2,3,4,5,done,done,done,done,done,...