4,4,5,7,9 - can anyone see the pattern, it’s driving me mad.

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These are the number of bars in 5 groups top to bottom in the towel rail in my bathroom. When I bought it I thought it was Fibonacci+3, now it’s driving me potty.

Of course there may be no pattern, but it would make my mornings much happier if there was.

Last edited by superluminary on 09 Dec 2013, 12:39 pm, edited 1 time in total.

It's an expression of the following algorithm. Step 1) create a sequence of numbers. Step 2) Arrange these numbers in such an order that will drive superluminary mad.

Hey, be gentle now

You can try using the Online Encyclopedia of Integer Sequences.

I just had a go at writing the algorithm, but am having trouble conceiving of it

Floor(n^2/3) + 4

Good tip!

{I'm not a math person, I'm more visual, but I do get obsessed with stuff like that. Another problem with it is it adds up to 29, which adds to 11, which adds to 2. And so, for me that would say: two fours stand for 2, but having two fours is annoying, so the (nice) odd numbers counteract them. I imagine the numbers re-arranged as 4, 5, 9, 7, 4. Then: I have a picture in my mind of the numbers represented by plain wooden blocks. I remove one block from the '7' pile, and place it on the '5' stack. That gives a visual pattern of 4, 6, 9, 6, 4.}

I am glad I don't look at that sequence in my bathroom.

I like that very much indeed!



It is right opposite the glass screen door in the shower, so every morning I have to spend 5 to 10 minutes contemplating it

Shhhhh!! !... you are blowing the whole conspiracy wide open!

Also, oh my goodness, there is an online encyclopedia of integer sequences. This is practically porn!

Separately, another pattern *might* be apparent: number of strokes to form the sequence......

4 = 3 strokes (3x)
5 = 3 strokes (1x)
7 = 2 strokes (1x)
9 = 1 stroke (1x)
7 = 2 strokes (1x)
> gives 2, 2, 1, 1

Then again, maybe it's just uneven tiles? What number comes next? And what comes before?

Counting integers 0 to 9, strokes are 1, 1, 1, 2, 3, 3, 1, 2, 1, 2, 1
...........................

It could be the following algorithm: A) Find all the solutions to the following pentic equation: Ax^5 + Bx^4 + Cx^3 + Dx^2 + Ex + F = 0. B) Take the absolute magnitude of all the solutions. C) Arrange the results from step B in ascending order.

The only thing is that I don't know what the values of A, B, C, D, E, and F would be. I guess it would involve taking the pentic formula and working our way backwards.

Or it could be the following algorithm: 1) List all the positive integers, including zero, in ascending order. 2) Now arrange these integers in a such a way that any integer N occurs N^N times. 3) List the number 4. 4) Take the number 4 and add the first number from the series described in step 2, and list it after 4. 5) Take the result from step 4 and add the second number from the series described in step 2, and list the result after the result from step 4. 6) Take the result from step 5 and add the third number from the series described in step 2. etc......

In other words: 4 - 4 = 0. 5 - 4 = 1. 7 - 5 = 2. 9 - 7 = 2. That's 0,1,2,2. 0 occurs one time because 0^0 is 1. 1 occurs one time because 1^1 is 1. 2 will occur 4 times, 3 will occur 27 times, 4 will occur 256 times, etc. Thus, take 4 and add 0 to it: 4, 4. Take 4 and add 1 to it. 4,4,5. Take 5 and add 2 to it. 4,4,5,7. Take 7 and add 2 to it. 4,4,5,7,9.

The next terms in that sequence should be 11, 13, 16, 19, 22....etc. In your case, the algorithm terminated after 7 steps.

There is no discernible pattern yet. More data is needed.

There are an infinite number of mathematical functions that will produce that sequence. So there is no one and unique answer.

ruveyn

As to your sequence, that's easy:

4+4-5+7-9=1



(I actually stopped at this topic because I had a vivid dream late in high school of which all I recalled upon waking was the phrase "4, 5, 7, 9, spetseo, spetseo, aiophilio, betseo". Weird and striking enough to stick with me for 20 years, and similar enough to your 4,4,5,7,9 sequence that I had to stop and comment. As far as I know, the "words" have no meaning or derivation. The phonology seems Greek or Russian, there's maybe some echo of the "penta-" root in "spetseo", and "bi-" in "betseo", which would yield 4,5,7,9,5,5,x,2... No idea what "aiophilio" could be. Doesn't seem to follow the pattern of the other "words" so maybe an operator?)

Anyway...

This is an important result in analysis, and key for many useful, fruitful proofs. Even given dozens or hundreds of additional numbers in the sequence, we could still come up with an infinite number of functions to generate it.

By the above result, we could also find this sequence in the decimal expansion of pi, for instance.