favorite patterns?

[pixelpuffin]

what are your favorite patterns
I've run code for all of my favorites and I'm bored so lets see some of yours
example pattern http://oeis.org/wiki/Polygonal_numbers
(the 823543 heptagonal number is 233333320000000 in base 7 :D (why 823543? because that's 7^7 duh))

[Mats]

0, 1, 5, 21, 85, 341, 1365, 5461, 21845, 87381, 349525, 1398101, 5592405,
 22369621, 89478485, 357913941, 1431655765, 5726623061, 22906492245,
 91625968981, 366503875925, 1466015503701, 5864062014805, 23456248059221, 
93824992236885

(4^n - 1)/3

I love this sequence because of its connection to the collatz conjecture. All these numbers will go 3n + 1 straight into a power of two and then repeatedly halve until they reach 1.