An "eta-sequence": a(n) = floor( (n+1)*sqrt(2) ) - floor( n*sqrt(2) ).

Terms

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