A081869 a(1)=2; for n>1, a(n)=2*a(n-1)-1 if that number is composite, a(n)=a(n-1)+1 otherwise.

2, 3, 4, 5, 9, 10, 11, 21, 22, 23, 45, 46, 91, 92, 183, 365, 729, 1457, 2913, 5825, 11649, 11650, 23299, 46597, 93193, 186385, 186386, 372771, 745541, 1491081, 2982161, 5964321, 5964322, 11928643, 23857285, 47714569, 95429137, 95429138, 190858275