TITLE: Publishing a Simple Paper as an Undergraduate
QUESTION [41 upvotes]: First off I apologize if this question does not belong here, I would be happy to hear about any better locations to post this on.
I am a (first year) undergraduate mathematics student, and I recently discovered some interesting properties hidden in certain families of sequences.  I ran these ideas past my math professors, and they said these are interesting ideas and the kind of thing I may want to consider publishing.  I did pretty thorough research through my school's library and I am highly confident at this point that these ideas have not been written on before.  
To give some context into the situation, I am attending a top 15 university, and my professors are all Harvard, Cambridge, Princeton, etc. educated, so I know they know what they are talking about.  With that said, the ideas I discovered -- while interesting -- are really pretty trivial as they can be completely understood with background in Calculus III and some linear algebra, and all my proofs fit onto about 3 pages of LaTeX.   
I would love to go ahead with trying to write up a paper on these ideas and get them published as I think that would be a great experience, however I do not want to run the risk of coming off as an over-confident "crank" type early on and be stained by that.  Would you recommend I keep my cards close to my chest so to speak, or do you think I should put my ideas out there and see what happens?  If I was to pursue publication, I would just submit to undergraduate journals, or maybe something else a little more specialized.

REPLY [11 votes]: To those journals already mentioned, I can add College Mathematical Journal published by MAA. But my advise is to ask those professors who approved your result. They must be able to give a good recommendation, after you show them the finished paper. In any case, I recommend you to show your finished paper to a professor.
I have similar experience: I wrote my first paper on my second undergraduate year.
I showed it to my professor, he recommended a (mainstream) journal, and the paper was accepted. Several of my friends mathematicians had a similar experience.