a(n) is the least k such that B(k^2) - B(k) = n, where B(m) is the binary weight A000120(m).

Terms

a(0) =0a(1) =5a(2) =11a(3) =21a(4) =45a(5) =75a(6) =217a(7) =331a(8) =181a(9) =789a(10) =1241a(11) =2505a(12) =5701a(13) =5221a(14) =11309a(15) =19637a(16) =43151a(17) =69451a(18) =82709a(19) =166027a(20) =346389a(21) =607307a(22) =689685a(23) =1458357a(24) =1380917a(25) =2507541a(26) =5906699a(27) =2965685a(28) =5931189a(29) =11862197