I have authored more than 3000 sequences in the OEIS. Here some of my favourites.

Number of 3-smooth numbers <= n

A self referential sequence related to Mancala solitaire

A self referential sequence related to Catalan tree

a(n) = floor((n+2)*phi) - floor((n+1)*phi)

The primes yielded by the previous sequence

A sequence yielding twin primes

Decimal expansion of the Kempner constant

a(1)=1, a(n) = a(n-1) + n * (sign(n-a(n-1))

Least x greater than 1 such that x^n == 1 (mod i) for each i=1,2,3,...,n.

Numbers n such that binary representation ends in an odd number of ones.

Numbers n such that Binomial(4n,n)/(3n+1) is not divisible by 4.

A family of curious periodic sequences

Least k>0 such that the last digit of (n+k)^n is the same as the last digit of n^n

Triangle read by rows giving coefficients of polynomials arising in successive differences of n!

Number of compositions of n into almost equal parts

Last digit of Fibonacci(n) is 1

Last digit of Fibonacci(n) is 2

Last digit of Fibonacci(n) is 3

Last digit of Fibonacci(n) is 4

Last digit of Fibonacci(n) is 5

Last digit of Fibonacci(n) is 6

Last digit of Fibonacci(n) is 7

Last digit of Fibonacci(n) is 8

Last digit of Fibonacci(n) is 9