The Thue constant is the transcendental number with binary expansion

(1)

(OEIS A014578), where, for positive integers , the th bit is 1 if is not divisible by 3 and is the ones' complement of the th bit if is divisible by 3. The initial zero in OEIS A014578 is not a bit of the fractional binary expansion. It is also given by iterating the substitution system starting with 1

			(2)
			(3)

Interpreted as a decimal number, the Thue constant equals 0.8590997968...(OEIS A074071).