MathLabs

Problem 5

Is it possible to choose 19831983 distinct positive integers, all less than or equal to 10510^5, no three of which are consecutive terms of an arithmetic progression? Justify your answer.
Step 1 of 4: Define the digit map
Previous stepNext step
an=(the binary digits of n)3a_n=(\text{the binary digits of }n)_3
Detailed analysis

For n≥1n\ge1, write nn in base 22 and interpret exactly the same digit string as a base-33 number; call the result ana_n. For example, 6=11026=110_2 gives a6=1103=12a_6=110_3=12.