A066747 Decimal expansion of the "binary" Copeland-Erdős constant 0.734121515408286120606...: concatenate primes in base two.

7, 3, 4, 1, 2, 1, 5, 1, 5, 4, 0, 8, 2, 8, 6, 1, 2, 0, 6, 0, 6, 2, 7, 8, 2, 8, 8, 4, 5, 7, 2, 3, 2, 1, 4, 9, 2, 2, 8, 5, 6, 5, 0, 4, 6, 6, 1, 1, 6, 1, 3, 9, 9, 1, 4, 0, 6, 6, 0, 3, 4, 1, 2, 5, 5, 5, 9, 5, 4, 0, 4, 5, 0, 4, 3, 7, 0, 0, 3, 1, 0, 8, 0, 6, 4, 3, 0, 6, 3, 4, 9, 2, 6, 9, 3, 2, 5, 6, 1, 6

Offset: 0

Author

Robert G. Wilson v, Jan 16 2002

Keywords

• nonn
• cons
• base

Comments

The "binary" Copeland-Erdős constant is obtained by concatenating the binary representations of the primes = 0.(10)(11)(101)(111)(1011)(1101)(10001)...

A theorem of Copeland & Erdős proves that this constant is 2-normal. - Charles R Greathouse IV, Feb 06 2015

Links

• A. H. Copeland and P. Erdős, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), pp. 857-860.

Crossrefs

Cf. A066748 (continued fraction), A191232 (binary digits).

Cf. A033308 (base-10 Copeland-Erdős constant).

Programs

Mathematica

a = {}; Do[ a = Append[a, IntegerDigits[ Prime[n], 2]], {n, 1, 100}]; RealDigits[ N[ FromDigits[ {Flatten[a], 0}, 2], 100]]

PARI

sum(n=1,25,(p=prime(n))*.5^s+=logint(p,2)+1,s=0)+printf("Accurate to %.0E",.5^s) \\ M. F. Hasler, Oct 25 2019