What are the next four numbers in the sequence of 
 1, 2, 3, 7, 15, 16 ? 

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Solution from Anon Jr.

Writing out the numbers we get
one, two, three, seven, fifteen, sixteen.

One, and two have lengths of three.
Three, and seven have lengths of five.
Fifteen, and sixteen have lengths of seven.

Continuing the pattern,
seventeen, and twenty-one have lengths of nine.
Twenty-three, and twenty-seven have lengths of eleven.

Therefore the next four terms are 17, 21, 23, and 27.