# What number comes next in this evenly doubled sequence?

I've been playing around with sequences lately and found a pretty evenly doubled sequence of single digit numbers:

1, 12, 30, 64, 65, 156, 175, 368, 369, 371, 752, 753, 1524, 1525, 3060, 3073, 6168, 6219, 6221, 12444, 12453, ...

##### Hints

The given sequence is generated using a repeating sequence. If we let $$G$$ represent this generating sequence, then the numbers $$G_0$$ and $$G_9$$ = $$1$$.

Can you tell me what number comes next, and why?

• single digit numbers? Oct 17 '21 at 1:42
• @DanielMathias yes, the answer is a sequence of single digit numbers, exposed by understanding the presented sequence. Oct 17 '21 at 11:45
• I assume it's not just the last digit, but it would technically work. Oct 17 '21 at 17:03
• @PiGuy314 you’ll have to elaborate on what you mean, but you are correct that it’s not just the last digit. Oct 17 '21 at 17:05
• I merely meant that the final digits of G0 and G9 were both 1. Oct 17 '21 at 17:10

WORK IN PROGRESS:

It must be around ....

24904 = = Double 1245 (= 2490) with 4 inserted somewhere

.... give or take a small increment.

Pattern:

In the Sequence, the Digits 1 to 9 appear in cyclic order, but at various Positions in each number.
The remaining Digits in each number form a Sequence that is either doubling or incrementing or both.
The Next number must be something like 2490 with 5 inserted somewhere and one Digit incremented like 24915 or 25905
Then the Next number must be something like Double with 6 inserted somewhere