# Staying grounded

I found a somewhat meaningful sequence that is not on OEIS yet, incredible!

Here are the first 100 numbers of this sequence:

 1,  2,  3,  4,  5,  6,  7,  8,  9,  2,
3,  5,  7,  9, 11, 13, 15, 17, 19,  6,
7,  8, 11, 14, 17, 20, 23, 26, 29, 12,
13, 14, 15, 19, 23, 27, 31, 35, 39, 20,
21, 22, 23, 24, 29, 34, 39, 44, 49, 30,
31, 32, 33, 34, 35, 41, 47, 53, 59, 42,
43, 44, 45, 46, 47, 48, 55, 62, 69, 56,
57, 58, 59, 60, 61, 62, 63, 71, 79, 72,
73, 74, 75, 76, 77, 78, 79, 80, 89, 90,
91, 92, 93, 94, 95, 96, 97, 98, 99,  4, …


Guess the next 10 numbers (and the pattern of course).

Hint 1:

I can write the pattern in eight words.

Hint 2:

Some mathematical purists would complain that I'm using an arbitrarily chosen standard. But this standard is used so often that many people don't even know about other ways to do it. These people could not solve this puzzle.

Hint 3, the first 1000 numbers of the sequence:

Will follow if nobody guesses it with the first 100 numbers.

• As a Hint for future puzzles don't add hints unless it becomes obvious they are needed. Either the hint is necessary to solve the puzzle (in which case its not a hint and should be part of the puzzle) or it is a way of making the puzzle easier which isn't needed before people have even had a go at solving it (or if you think it is too hard then again, incorporate the hints into the puzzle itself)! This is a great puzzle though. Jan 24, 2019 at 16:56

I think you are

Recasting the decimal representation of the numbers in the lowest possible base.

So for example

The decimal number 10, is also a number in base 2 (lowest possible) and is just 2.

The next 10 numbers will be

5, 11, 19, 29, 41, 55, 71, 89, 109, 6

i.e, 101 in base 2, 102 in base 3, 103 in base 4, 104 in base 5, etc

Title

This explanation also fits the title as instead of viewing each number in a higher base (10) we ground the number to its lowest possible. Thanks, Omega Krypton for the prompt.

• this also explains the title, you can also add it in your answer ;) +1 Jan 24, 2019 at 10:33
• Awww, that was apparently too easy, you solved it in less than 6 minutes. :D I also like that interpretation of the title, what I really thought was just "something with 'base'". What do you think, how many numbers in the sequence would have been enough to guess it? Jan 24, 2019 at 10:38
• I'm sorry I solved it quickly, it sometimes is just luck on whether somebody hits upon the right idea or not, this is a very clever puzzle. The fact that there is a drop every 10 did indicate that it had something to do with base. The big clue was dropping from 99 to 4 and maybe omitting that would make it slightly harder. Jan 24, 2019 at 10:50