a(n) = n-2 + Sum_{i = 1..n-2} (a(i+1) mod a(i)) for n >= 3 with a(1) = a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =5a(6) =8a(7) =12a(8) =17a(9) =23a(10) =30a(11) =38a(12) =47a(13) =57a(14) =68a(15) =80a(16) =93a(17) =107a(18) =122a(19) =138a(20) =155a(21) =173a(22) =192a(23) =212a(24) =233a(25) =255a(26) =278a(27) =302a(28) =327a(29) =353