a(n) = n XOR (n-1), i.e., nim-sum of sequential pairs, written in binary.

Terms

a(0) =1a(1) =11a(2) =1a(3) =111a(4) =1a(5) =11a(6) =1a(7) =1111a(8) =1a(9) =11a(10) =1a(11) =111a(12) =1a(13) =11a(14) =1a(15) =11111a(16) =1a(17) =11a(18) =1a(19) =111a(20) =1a(21) =11a(22) =1a(23) =1111a(24) =1a(25) =11a(26) =1a(27) =111a(28) =1a(29) =11