Number Sequence Challenge

1) They both have 8 numbers in them

2) All the numbers are Arabic, and none prime, because

3) They are both multiples of the same data set (1,2,3,5,8,13,21), and

When the first is subtracted from the second, you get the original data set

Each subsequent number is the sum of the preceding 2 numbers.

Hello 3Doug:

Take the second figure and add the previous figure:

4+2=6+4=10+6=16+10=26+16=42..........

6+3=9+6=15+9=24+15=39+24=63..........

OK?

Have a great new year.............

Do you have some more complex question? This one is too trivial.

Nick name,

may be something like this?

1, 2, 6, 42, 1806.....

Regards and happy new year for all!!!!

Ernesto

Term Tn+1= Tn*(Tn+1)

Also trivial, more complex please.

Happy new year

1, 11, 21, 1211, ...?

On both sequences you must add the number between the second and the first number and add it to the second and so on.

HAPPY NEW YEAR

As already pointed out, very trivial.......

Okay, I made this one too easy. Maybe. What I was wanting was to see if anyone could figure out how I got from the first number to the second. In the standard Fibonacci sequence, you start with two consecutive numbers, I believe, before you start adding. This should still be easy. I promise to come up with something harder in a day or two. I do have an idea, but it needs work.

when I first looked at this, I thought, each of these sequences is produced by multiplying the initial number times the 'classic' (??) fibonacci series beginning with 1... ?

easy is ok for us non-maths types who feel fantastic just for recognizing fibonacci at all... time spent with math nuts is not totally wasted then...

Well, it looks as if no one is going to venture a guess on how I went from n₁ to n₂, so I'll go ahead and offer up the number sequence I was thinking of.

What are the next four numbers in this sequence, and how do you determine them?

2 ,3, 5, 7, 12, 13, 25, 38, 41, 79, 120, 127, 247, 374,....

Yes, this is a sequence that matches a pattern, and it is not just a set of random or pseudo-random numbers.

Your pattern is not consistent so that a lot of possibilities are open I made a choice which I do not know if it was yours:

399 773 1172 1845

With a consistent pattern from the start the series should have been:

2 3 5 8 10 18 28 33 61 94 112 206 318 412 730 1142 1872

If the feed back pattern evolution is changed the numbers are different.

Happy new year to you

Interesting that you used the term "feed back." The pattern does have a trigger that initiates changes in the pattern, but I am not sure if you would call it feedback.

I will give one clue on the entire sequence: it starts with a finite set of numbers that are given in sequence. The pattern in the rest of sequence uses elements of the finite set.

I have to go take care of some business now, but when I get back, if you haven't figured out anything more about the sequence, I'll extend the sequence to give you more data to work with. As Charlie Epps says in Numb3rs, "More data often gives better results."

Here's the expanded sequence:

2 ,3, 5, 7, 12, 13, 25, 38, 41, 79, 120, 127, 247, 374, 379, 753, 1132, 1151, 2283, 3434, 3449, 6683, 10132, 10133, 20265, 30398, 30403,...

To find the "triggers" I mentioned, look for the numbers that stick out.

I still maintain that your approach is not consistent and I shall show why I write it.

You start a sequence with no actual relation 2;3;5 &7.

12=7+5

13=12+1 It is the 1st break in the building sequence

25=13+12

38=25+13

41=38+3 2nd break

79=41+38

120=79+41

127=120+7 3rd break If you compare with break 4 then you should have here 5 and at break 4 7

247=127+120

374=247+127

379=374+5 4th break

The procedure is:

for 2 successive steps T(j)=T(j-2)+t(j-1)

Every 2 steps T(j)=T(j-1)+N Nbeing a number from an other sequence. This I recognised from the 1st time but I thought that you used as "N" numbers from the beginning of the sequence which would have been much more complex to find ans I also assumed that the numbers were collected at progressively augmented distances in the sequence. In fact both approaches are possible.

What I consider as non consistent is that the second sequence is a not progressive sequence since the values go up than down and come to same values. On my opinion the second sequence could have been either the sequence of not even numbers or a geometric sequence or an alternated sequence of even and not even numbers but with same trend.

The building of the sequence does not start from the beginning and you have a number of terms not aacording to your building procedure.

A consisten sequence would have been:

2 3 5 8 9 17 26 29 55 84 89 173 262 269 531 800 809.....

2&3 as seeds 5=2+3 8=5+3 9=8+1 and so on.

For this sequence all is consistent.

A Happy New Year to you

My pattern is consistent because 2, 3, 5, and 7 do have a relationship. They are a finite set of numbers that have two characteristics in common. One characteristic is obvious, the other should be as well.

After listing the set in sequence, I applied a rule to begin the pattern. If there is a universal rule that all numbers in a given sequence must conform to a given pattern, then I am unaware of it. But considering that this sequence could be used in cryptography, and the introduction of an extra factor will produce a more unbreakable code or cipher, I feel I am at liberty to ignore such a rule, as long as the exception makes sense.

Look at the numbers that come up when the pattern changes for the next clue.

You are right!

I guess it's time to wrap this up.

My original sequence was a regular Fibonacci series with the first two numbers being n and 2n. What I failed to realized that a Fibonacci sequence could start with any two numbers, and the standard Fibonacci sequence starts with 1 and 2, which also meet the n and 2n. I should have started with larger values for n, but it would have still been too simple.

For the second sequence, I started with a finite set of numbers, started a Fibonacci sequence, but when a result met a certain condition, I jumped to the next number that met a particular condition, and restarted the Fibonacci series. The finite set was single-digit primes. The "triggers" for the jumps were even numbers. The values jumped to were primes. The next four numbers in the sequence are 60801, 91204, 91229, and 182433. Because the values increase so fast, I suppose one could use this as part of an algorithm to find candidates for large primes very fast, but you would have to add a test for primacy. And as I stated in a previous post, I imagine this could also be used to generate a very hard-to-break cipher or code.

And speaking of cryptography, I have an idea for a cipher that I might use for another challenge later on.

nick name, thanks for hanging in there. I sometimes enjoy being sneaky, ambiguous and obscure, and I know how annoying that can be. I hope I didn't exasperate you too much.