Are there any known facts/particularities/theorems about structures as the one below?

$$ 3^0 \cdot 2^{a_0} +3^1 \cdot 2^{a_1} + ... + 3^n \cdot 2^{a_n} $$

$$ n, a_0, a_1, .. a_n \in N $$

MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.

Sign up to join this community
Anybody can ask a question

Anybody can answer

The best answers are voted up and rise to the top

$\begingroup$
$\endgroup$

Are there any known facts/particularities/theorems about structures as the one below?

$$ 3^0 \cdot 2^{a_0} +3^1 \cdot 2^{a_1} + ... + 3^n \cdot 2^{a_n} $$

$$ n, a_0, a_1, .. a_n \in N $$

$\begingroup$
$\endgroup$

This looks similar to numerators of fractions with odd denominator that create specific Collatz cycles. See: Collatz Conjecture: Iterating with odd denominators or 2-adic integers (Wikipedia)