Blue numbers!

My opinion is that your are int eh Science & Mathematics forum.

That's just an opinion, of course.

Point taken Roger, with over 6400 posts, your opinion is more valid than mine is.
However, I doubt whether the Riddles forum is on any Mathematicians check list and this particular topic may appeal to some of the knowledgeable members who would otherwise be unaware of its existence.

Ok, I'll bite. What's a blue number?

I think it's kind of like a sleezy strip act. Like your new Avatar, by the way.

Seniority counts for nothing, Tryagain. Nothing.

thanks roger.

Roger writes, "Seniority counts for nothing, Tryagain. Nothing."

I apologise in advance, however, I fee I have to disagree with that statement because it is due to you and members like you who contribute so freely to this site that makes it what it is.

In an effort to avoid any misinterpretations regarding ?'Blue Numbers' I reproduce the math problem produced by Whimsical:


"If you can write a number as a sum of at least two consecutive positive integers we call it a Blue number.

Examples:
9=4+5, so 9 is called a blue number
10=1+2+3+4, 10 is called a blue number


Question: Can you find all the numbers that can't be called blue numbers
between 1000 and 2000 and prove your answers."


I thought, perhaps mistakenly, that it might appeal to inquiring minds. If I was wrong, I apologise again.

Huh. That's an interesting problem. On inspection it looks like all numbers of the form 2^X between 1000 and 2000. I'll have to think on it and try to prove it. It's interesting, Tryagain, thanks for posting it.

The thanks go to Whim, the originator of this unique question. I hope you enjoy the challenge of finding the proof. There is already a possible answer on the original post. Good luck.