A100125 Decimal expansion of Sum_{n>0} n/(2^(n^2)).

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

Offset: 0

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

Keywords

• cons
• nonn

Comments

This number is obviously 2-dense, but not 2-normal: any finite binary string s representing the value N will appear in its digits, not later than those added by the term N/2^(N^2), but nonzero digits have density zero since the gap between those added by subsequent terms is increasing much faster (~ n) than the maximal possible number of new nonzero digits (~ log_2(n)). - M. F. Hasler, Mar 22 2017

Examples

			0.6309205592551858647783240039079433700921514299217879868...
		

Links

• David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, page 27.

Crossrefs

Cf. A066716: binary Champernowne constant.

Programs

Mathematica

RealDigits[N[Sum[n/(2^(n^2)), {n, 4!}], 100]][[1]] (* Arkadiusz Wesolowski, Sep 29 2011 *)

PARI

default(realprecision,100);sum(n=1,100,n/(2^(n^2)),0.) \\ Typo corrected. sum(n=1,100,n*1.>>(n^2)) is 25 x faster for 1000 digits. - M. F. Hasler, Mar 22 2017

Extensions

Offset corrected by Arkadiusz Wesolowski, Sep 29 2011