Question 90
A sequence of positive integers $\{s_i\}$ is constructed in the following way: $s_1 = 2$, and for all $i \gt 1$ $s_i$ is the least number that is larger than $s_{i-1}$ and contains digit:
* "2" if $i = 1$ (mod 4)
* "0" if $i = 2$ (mod 4)
* "1" if $i = 3$ (mod 4)
* "4" if $i = 4$ (mod 4).
This sequence starts with $2$, $10$, $11$, $14$, $20$, $30$, $31$, $34$, $42$, $50$, ...
Does $\{s_i\}$ contain number
a) $2001$
b) $2004$?
* "2" if $i = 1$ (mod 4)
* "0" if $i = 2$ (mod 4)
* "1" if $i = 3$ (mod 4)
* "4" if $i = 4$ (mod 4).
This sequence starts with $2$, $10$, $11$, $14$, $20$, $30$, $31$, $34$, $42$, $50$, ...
Does $\{s_i\}$ contain number
a) $2001$
b) $2004$?