What is the next number in sequence?

Question

Consider the following sequence:

6211, 4214, 6321, 4135, 6359

What is the next number in that sequence? What are the rules of that sequence?

I hope you'll enjoy my first question :)

Sorry guys, with those numbers, it is impossible to find the next one. So I have added the next one so it becomes possible.

The new sequence is:

6211, 4214, 6321, 4135, 6359, 4182

Here is a hint:

Some numbers where chosen to confuse you. You shouldn't focus on them, but focus on the whole.

$\begingroup$ Are you sure it's supposed to be 6359 and not 6350? $\endgroup$
– user88
Commented Apr 20, 2015 at 22:47 — user88, Commented Apr 20, 2015 at 22:47
$\begingroup$ Yes, I am sure. $\endgroup$
– A.D.
Commented Apr 20, 2015 at 22:50 — A.D., Commented Apr 20, 2015 at 22:50
$\begingroup$ Are you sure it's supposed to be 6359 and not 6459? $\endgroup$
– user88
Commented Apr 20, 2015 at 23:06 — user88, Commented Apr 20, 2015 at 23:06
$\begingroup$ Yes, I am sure. $\endgroup$
– A.D.
Commented Apr 20, 2015 at 23:12 — A.D., Commented Apr 20, 2015 at 23:12

score 4 · Accepted Answer · 2015-04-20 23:34:24Z

4

The seventh number is 6136.

The last digit of each number is the $n$th digit after the decimal point of $\pi$.

The first three digit numbers follow this pattern:

Place the $n$th Fibonacci number so that the ones' digit is the third digit of the number.
Then, insert digits so that the sum of the digits of the sum of the digits of the number is equal to to $n$. If the $n$th Fibonacci number is less than 10, then use a sequence alternating $6$ and $4$ to fill in the first digit, and then fill in the second digit as appropriate.

So the eleven terms of the sequence would be:

6211, 4214, 6321, 4135, 6359, 4182, 6136, 9215, 8343, 4555, 4898

The sequence ends there since the next Fibonacci number is 144 which would no longer ensure the sum-of-digits rule to be intact.

answered Apr 20, 2015 at 22:50

user88

$\begingroup$ Argh, beat me to it. $\endgroup$
– Tryth
Commented Apr 20, 2015 at 22:51
$\begingroup$ Your solution pinning $4$ as the second digit seems a bit iffy. $\endgroup$
– user88
Commented Apr 20, 2015 at 22:51
$\begingroup$ If you look at the update I've made, you'll see you're on the right tracks :) $\endgroup$
– A.D.
Commented Apr 20, 2015 at 22:54
$\begingroup$ You have all the information you need to solve it. There is no unknown sequence of number involved. $\endgroup$
– A.D.
Commented Apr 20, 2015 at 23:02
1

$\begingroup$ The fact the all the 2nd numbers are $\le 4$ makes me think the 2nd number might be self-referential in some way. $\endgroup$
– Tryth
Commented Apr 20, 2015 at 23:02

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