Find a recursive and a non-recursive definition for the sequence: 3, 4, 13, 14, 23, 24, …

Answer 1

The sequence is 3,4,13,14,23,24,33,34,43,44,53,54,...

Now the sub-sequence of the evens is 3,13,23,33,43,53,... and the sub-sequence of the odds is 4,14,24,34,44.54,...

Then the explicit form (what you call the non-recursive definition) of the sequence is

a(n)=3+10(n-1) if n is even and a(n)=4+10(n-1) if n is odd

I don't think there is a recursive expression for this specific sequence.