Spoiler:
1+1=3 , (01+01)+1=03
3+3=7 , (03+03)+1=07
7+7=15 , (07+07)+1=15
15+15=31, (15+15)+1=31
Next three for fun
(031+031)+1= 063
(063+063)+1= 127
(127+127)+1= 255
255+1=256 = 2 ^ 8
127+1=128 = 2 ^ 7
063+1=064 = 2 ^ 6
031+1=032 = 2 ^ 5
015+1=016 = 2 ^ 4
007+1=008 = 2 ^ 3
003+1=004 = 2 ^ 2
001+1=002 = 2 ^ 1
3+3=7 , (03+03)+1=07
7+7=15 , (07+07)+1=15
15+15=31, (15+15)+1=31
Next three for fun
(031+031)+1= 063
(063+063)+1= 127
(127+127)+1= 255
255+1=256 = 2 ^ 8
127+1=128 = 2 ^ 7
063+1=064 = 2 ^ 6
031+1=032 = 2 ^ 5
015+1=016 = 2 ^ 4
007+1=008 = 2 ^ 3
003+1=004 = 2 ^ 2
001+1=002 = 2 ^ 1