Mathematics, applications of mathematics to life in general, and my life as a mathematician.

Found the following cute puzzle on Facebook.

Puzzle. Discover the rule governing the following sequence to find the next term of the sequence: 8, 3, 4, 9, 3, 9, 8, 2, 4, 3.

6,7

…4,4,2,3,8

That was fun!

…4,5,3,5,4,2,6,3,4,7,3,7,6,2,8,3,4,9…

…,1,9,5,2,4…

… 4, 6, 3

but I’m not sure .. what is the reasoning behind?

One of the five answers above is correct. Hint: The rule is simple. If you are not sure, you didn’t discover it.

Blaine has it. Unfortunately I don’t see a way to determine additional terms… unless they are 1, 1, 1…?

Michael, perhaps it could continue as 5, 5, 4, 4, 5, 4, 5, 3… and would it eventually devolve into 4, 4, 4… ?

Mmmh, I don’t follow

Hint: This is a self-referencing puzzle.

I got it; however, my very simple (and human language-independent!) program says 1,9,5,2,4.

Indeed, the rational number with the lowest denominator, which decimal form starts with .8349398243 is 138681/166097 = 0.83493982431952413348…

…4,4,2,3,9(or 8) ?

I see the mirror rule a(i)=a(13-i)+1 for i<13-i, i!=4. This would continue with two terms: 2 and 7. But this is different to all given ones and Tanya said the good is already given.

Hint: ignore the word “Puzzle” and proceed from there.

Oh! I see now, nice. Not as much a self-referencing puzzle as a prelude-referencing one, I would say.

…8

And perhaps a couple of 1’s if you’re so inclined 🙂

..4, 4, 2, 3, 8.

And perhaps a couple of 1’s if you’re so inclined… 🙂

Meh, its not in the OEIS, so most likely not given by some easy formula…

This is fun, I am sure the next few terms according to this rule would be 4, 2, 3, 1, 2, 4, 3 , 4, 3, 5, 9

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## Alex:

6,7

31 December 2020, 8:55 pm## Blaine:

…4,4,2,3,8

That was fun!

1 January 2021, 1:51 am## gabriella:

…4,5,3,5,4,2,6,3,4,7,3,7,6,2,8,3,4,9…

1 January 2021, 6:28 am## Leo B.:

…,1,9,5,2,4…

1 January 2021, 10:22 pm## Robert:

… 4, 6, 3

but I’m not sure .. what is the reasoning behind?

2 January 2021, 5:37 am## tanyakh:

One of the five answers above is correct. Hint: The rule is simple. If you are not sure, you didn’t discover it.

2 January 2021, 1:17 pm## Michael:

Blaine has it. Unfortunately I don’t see a way to determine additional terms… unless they are 1, 1, 1…?

3 January 2021, 4:06 pm## Blaine:

Michael, perhaps it could continue as 5, 5, 4, 4, 5, 4, 5, 3… and would it eventually devolve into 4, 4, 4… ?

4 January 2021, 10:19 am## Richard:

Mmmh, I don’t follow

6 January 2021, 5:10 am## tanyakh:

Hint: This is a self-referencing puzzle.

6 January 2021, 2:47 pm## Leo B.:

I got it; however, my very simple (and human language-independent!) program says 1,9,5,2,4.

Indeed, the rational number with the lowest denominator, which decimal form starts with .8349398243 is 138681/166097 = 0.83493982431952413348…

7 January 2021, 1:47 am## Stefano:

…4,4,2,3,9(or 8) ?

9 January 2021, 12:23 pm## Cristóbal Camarero:

I see the mirror rule a(i)=a(13-i)+1 for i<13-i, i!=4. This would continue with two terms: 2 and 7. But this is different to all given ones and Tanya said the good is already given.

25 January 2021, 7:29 am## Blaine:

Hint: ignore the word “Puzzle” and proceed from there.

8 February 2021, 12:56 am## Cristóbal Camarero:

Oh! I see now, nice. Not as much a self-referencing puzzle as a prelude-referencing one, I would say.

8 February 2021, 4:42 pm## Marnix:

…8

And perhaps a couple of 1’s if you’re so inclined 🙂

10 February 2021, 4:29 am## Marnix:

..4, 4, 2, 3, 8.

And perhaps a couple of 1’s if you’re so inclined… 🙂

10 February 2021, 4:31 am## Per:

Meh, its not in the OEIS, so most likely not given by some easy formula…

7 May 2021, 4:55 pm## Taposik:

This is fun, I am sure the next few terms according to this rule would be 4, 2, 3, 1, 2, 4, 3 , 4, 3, 5, 9

8 July 2021, 2:09 am