

A100125


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


1



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
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OFFSET

0,1


COMMENTS

This number is obviously 2dense, but not 2normal: 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


LINKS

Table of n, a(n) for n=0..99.
David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, page 27.


EXAMPLE

0.6309205592551858647783240039079433700921514299217879868...


MATHEMATICA

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


PROG

(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


CROSSREFS

Cf. A066716: binary Champernowne constant.
Sequence in context: A206530 A333549 A191896 * A153459 A102525 A119923
Adjacent sequences: A100122 A100123 A100124 * A100126 A100127 A100128


KEYWORD

cons,nonn


AUTHOR

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


EXTENSIONS

Offset corrected by Arkadiusz Wesolowski, Sep 29 2011


STATUS

approved



