#odiousnumber — Public Fediverse posts

For #genuary18, the prompt is an unexpected path that follows a very simple rule. My "simple" rule returns to the concept of "odious numbers": if ⌈x⋅y⌉ is odious, turn 60 degrees counterclockwise. Otherwise, turn 60 degrees clockwise. Here, three paths with different initial points are traced for 1000 iterations of this rule.

#genuary #genuary2026 #odiousnumber

I had to look up today's #mathober prompt, "odious", to see what it meant in a mathematical context. I learned that an "odious number" has an odd number of 1's in its binary representation. Then I wondered if anyone had extended that to other number bases. What if the number of (N-1) digits in a number represented in base N is not divisible by N? For N=2, this becomes the same definition as an odious number.

This image visualizes the N-odious numbers for N=2 through N=5 in a spiral akin to Ulam's Prime spiral. The regular odious N=2 case are the smallest red dots, with the dot size increasing up to N=5. Maybe I'll call these "noisome numbers" just for fun.

#mathober #mathart #odiousnumber #noisomenumber #numbertheory