Ternary and decimal expansion of an integer solely

ab0utfallingm1z2

ab0utfallingm1z2

Answered question

2022-04-01

Ternary and decimal expansion of an integer solely consists of 2 and 0.

Answer & Explanation

Jermaine Lam

Jermaine Lam

Beginner2022-04-02Added 11 answers

Step 1
I think they will run out after a while. This is not a proof, just heuristics.
There are 2n of these numbers of length n+1. One approach is to think of the base 3 version as a random set of digits. There will be about (n+1)log310 base 3 digits each has 23 chance of being 0 or 2
The chance of any of the n+1 digit decimal numbers being just 0s and 2s in ternary would be
C223log310n C(0.855n)
This has a finite sum, so I expect finitely many of these numbers.

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