Prime Constant

The characteristic function

(1)

of primes has values 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ... (OEIS A010051) for , 2, .... The constant obtained by concatenating these digits and interpreting them as a binary fraction is therefore

			(2)
			(3)

(OEIS A051006).

The continued fraction is [0, 2, 2, 2, 3, 12, 131, 1, ...] (OEIS A051007). It has high-water marks of 0, 2, 3, 12, 131, 169, ... (OEIS A102878), occurring at positions 0, 1, 4, 5, 6, 20, 31, 54, ... (OEIS A103313).

REFERENCES:

Sloane, N. J. A. Sequences A010051, A051006, A051007, A102878, and A103313 in "The On-Line Encyclopedia of Integer Sequences."