OFFSET
0,1
COMMENTS
David H. Bailey and Richard E. Crandall proved that Stoneham numbers S(b,c) = Sum_{k>=1} 1/b^(c^k)/c^k are b-normal under the simple condition b,c > 1 and coprime. So the present number is 2-normal.
REFERENCES
David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, 2000.
LINKS
David H. Bailey and Richard E. Crandall, Random Generators and Normal Numbers, Experimental Mathematics, vol. 11, no. 4 (2004), pp. 527-546; LBNL-46263.
R. Stoneham, On the Uniform Epsilon-Distribution of residues Within the Periods of Rational Fractions with Applications to Normal Numbers, Acta Arithmetica 22 (1973), 371-389.
FORMULA
S(3, 2) = 0.000011110..
MATHEMATICA
digits = 100; Clear[s]; s[n_] := s[n] = (rd = Sum[1/3^(2^k)/2^k, {k, 1, n}] // RealDigits[#, 2, digits]&; Join[Table[0, {Last[-rd]}], First[rd]]); s[1]; s[n=2]; While[s[n] != s[n-1], n++]; s[n] (* Jean-François Alcover, Feb 15 2013 *)
PROG
(PARI) binary(sum(k=1, 6, 1./3^(2^k)/2^k))
CROSSREFS
KEYWORD
AUTHOR
Benoit Cloitre, Aug 10 2003
STATUS
approved