a(2n) = 2*4^n-1, a(2n+1) = (2^(n+1)+1)^2; interlaces A083420 with A028400.

Terms

a(0) =1a(1) =9a(2) =7a(3) =25a(4) =31a(5) =81a(6) =127a(7) =289a(8) =511a(9) =1089a(10) =2047a(11) =4225a(12) =8191a(13) =16641a(14) =32767a(15) =66049a(16) =131071a(17) =263169a(18) =524287a(19) =1050625a(20) =2097151a(21) =4198401a(22) =8388607a(23) =16785409a(24) =33554431a(25) =67125249a(26) =134217727a(27) =268468225a(28) =536870911a(29) =1073807361