# How to articulate the answer to the 82k sequence riddle

I have found the quintessential you-won't-find-it-if-you-don't-know-it question:

Question: "What is the next element of this sequence: 2,3,4"

82000

Short explanation:

2 is the minimum integer $$>1$$ that can be written in base 2 only using digits 0 and 1.
3 is the minimum integer $$>1$$ that can be written in bases 2,3 only using digits 0 and 1.
4 is the minimum integer $$>1$$ that can be written in bases 2,3,4 only using digits 0 and 1.
82000 is the minimum integer $$>1$$ that can be written in bases 2,3,4,5 only using digits 0 and 1.

Long explanation & source:

Now my question is: How can I articulate a small answer well? Notice how the current "Short explanation" is very repetitive. It is (kinda) easy to grasp, sure, but I'd rather have an opening "condensed" version first, and then explain further.

The nth element of the sequence is

the smallest integer >1 that, when written in every base up to n + 1, uses only the digits 0 and 1.

Alternatively, if you use an offset such that the first term has n=2, you could say

the smallest number > 1 whose representation in all bases up to n consists only of zeros and ones.

Source for the second solution: https://oeis.org/A258107

• neat........... – George Menoutis May 7 at 8:49
• Does this factor in that it must be >1 ? – Jay May 7 at 11:24
• Ah yes. I’ve amended my answer – MichaelMaggs May 7 at 11:47