On-Line Encyclopedia of Integer Sequences

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In this thread, you can talk about integer sequences that fascinate you. One of the sequences that interested me was the sequence of palindromes in base 10 (A002113); I think there's something special about a series of symbols that can be read the same way backwards and forwards.

Oh yes, I love those. :]

Well I can make anything happen in fives, divisible by or are a multiple of five, or directly or indirectly appropriate to 5.

One I recently discovered was strictly not a single sequence, but rather a lot of sequences in one construction.

In Pascal's Triangle( A001316) you can find counting numbers, triangle numbers, powers of two, Fibonacci numbers and probably more!

It also helped me out in a programming task were you had a grid of N x N nodes and the task was to find the number of possible paths from top left to bottom right moving only down or right. If I remember correctly, the answer for each value was in the single cells ( 2, 6, 20, 70, ... ) So for 2 x 2 there are 2 possible paths. 3 x 3 there are 6 etc...

Back in my early days on WP, I used to post my favorite Primes and I would also cite OEIS for various prime generating
Polynomials that show their relationship to other primes.

http://mathworld.wolfram.com/Prime-Gene ... omial.html

Another source is Wolfram Alpha.

I love oeis.org . I did my undergraduate degree in math,but am now studying statistics for my masters. I still try to mess around with some math on occasion though.

One neat thing about oeis.org is that if you come up with a sequence plug it into oeis you not only get what the sequence is but you also get which combinatorial objects they are related to.

I was trying to find the number of "instruments" with k items and n levels as it turns out this was the number was already found by Euler, although the impetus for him was slightly different.

I really love partition theory. the number of partions of a number is given by this sequence A000041.
I try to come up with new generating functions sometimes and I use maple to calculate the first k coefficients.
I suggest looking into partitions they are very neat, there are some really really beautiful identities, theorems etc on contained in this field. Also in q-series (which generally has to do with partition theory), there are many neat q analogs to things like binomial coefficients and the gamma function.

I also like A000040 (prime numbers) and A000045 (Fibonacci numbers).

In the Year 2525 (A111729)
Cake Numbers (A000125)
Lazy Caterer's Sequence (A000124)

When I was a grad student in Math in the 1970s, one of the profs had a deck of punch cards with one prime number per card. I think that it had all the prime numbers less than 100,000 in the deck. One of his grad students was throwing it away so I asked if I could have it so he gave it to me.

The next problem was what to do with it.

So for a week or so, I carried a stack of punch cards from it with me and would walk up to people and giving them their very own prime number.

At first people were surprised and tolerated it, but after I had given them two or three prime numbers they started to get pretty mad at me and I had to quit.

I don't remember how many prime numbers i gave away in that few days, but when I was through, the deck was quite a bit smaller than when I started.

A212693 - Number of legal 7 X 6 Connect-Four positions after n plies.

A000796 (Decimal expansion of pi, or digits of pi)

square pyramidal numbers (sequence A000330 in OEIS)
triangular pyramidal numbers (sequence A000292 in OEIS)