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

0,1

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

Table of n, a(n) for n=0..99.

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A169813 A097517 A127559 * A240908 A117043 A013664

Adjacent sequences: A066744 A066745 A066746 * A066748 A066749 A066750

Keyword

nonn,cons,base

Author

Robert G. Wilson v, Jan 16 2002

Status

approved