A028948 An "extremely strange sequence": a(n+1) = [ A*a(n)+B ]/p^r, where p^r is the highest power of p diving [ A*a(n)+B ] and p=2, A=4.001, B=1.2.

1, 5, 21, 85, 341, 1365, 2731, 10927, 5465, 10933, 1367, 2735, 10943, 5473, 10949, 1369, 2739, 10959, 5481, 10965, 1371, 2743, 10975, 5489, 10981, 1373, 2747, 10991, 5497, 10997, 1375, 2751, 11007, 5505, 11013, 1377, 2755, 11023