I am also interested in integer sequences, e.g. the prime numbers, i.e. 2, 3, 5, 7, 11, 13, etc.  The On-line Encyclopedia of Integer Sequences http://oeis.org/ is a highly useful tool for researching topics that include integer sequences.  There are many sequences in the OEIS but I managed to author 3 new ones so far;

My 1st integer sequence For increasing z>0, integers, y-x, where x^3 + y^3 = z^3 + 1, with y>x>1.

My 2nd integer sequence Integers n where n^3 + (n+1)^3 is a Taxicab number A001235.

My 3rd integer sequence First differences of A006878 (record new trajectory lengths of Collatz function) (Hailstone sequence).