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A066716 The "binary" Champernowne constant. 4
8, 6, 2, 2, 4, 0, 1, 2, 5, 8, 6, 8, 0, 5, 4, 5, 7, 1, 5, 5, 7, 7, 9, 0, 2, 8, 3, 2, 4, 9, 3, 9, 4, 5, 7, 8, 5, 6, 5, 7, 6, 4, 7, 4, 2, 7, 6, 8, 2, 9, 9, 0, 9, 4, 5, 1, 6, 0, 7, 1, 2, 1, 4, 5, 5, 7, 3, 0, 6, 7, 4, 0, 5, 9, 0, 5, 1, 6, 4, 5, 8, 0, 4, 2, 0, 3, 8, 4, 4, 1, 4, 3, 8, 6, 1, 8, 1, 3, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

Eric E. Weisstein, Binary Champernowne Constant

FORMULA

The "binary" Champernowne constant is the number whose base-2 expansion is the concatenation of the binary representations of the integers, 0.(1)(10)(11)(100)(101)(110)(111)(1000)..., cf. A030302.

EXAMPLE

0.8622401258680545715577902...

MATHEMATICA

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

PROG

(PARI) my(s=0.); forstep(n=default(realprecision), 1, -1, s=(s+n)>>#binary(n)); s \\ Charles R Greathouse IV, Feb 06 2015, corrected by M. F. Hasler, Mar 22 2017

(PARI) s=0; sum(n=1, 31, n*.5^s+=#binary(n)) \\ Accurate to the given precision if s > default(realprecision)*log(10)/log(2). The sum up to n=31 is enough for standard precision of 38 digits. - M. F. Hasler, Mar 22 2017

CROSSREFS

Cf. A033307, A030190.

Cf. A030302: binary digits, A030190: same with initial 0, A030303: indices of 1's, A007088, A047778 (concatenate binary 1..n).

Cf. A100125: Sum n/2^(n^2).

Sequence in context: A272430 A021120 A021541 * A272006 A033952 A021847

Adjacent sequences:  A066713 A066714 A066715 * A066717 A066718 A066719

KEYWORD

cons,nonn,base

AUTHOR

Robert G. Wilson v, Jan 14 2002

EXTENSIONS

Leading zero removed, offset adjusted, and keyword:cons added by R. J. Mathar, Mar 04 2010

STATUS

approved

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Last modified June 24 05:21 EDT 2019. Contains 324318 sequences. (Running on oeis4.)