OFFSET
0,7
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 normal in base 10.
LINKS
D. H. Bailey and R. E. Crandall, Random Generators and Normal Numbers, Exper. Math. 11, 527-546, 2002.
R. Stoneham, On the Uniform Epsilon-Distribution of residues Within the Periods of Rational Fractions with Applications to Normal Numbers, Acta Arithmetica, Vol. 22, No. 4 (1973), pp. 371-389.
FORMULA
S(3, 10) = 0.00000169350878084302...
MATHEMATICA
digits = 99; Clear[s]; s[n_] := s[ n] = (rd = Sum[1/3^(10^k)/10^k, {k, 1, n}] // RealDigits[#, 10, 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) sum(k=1, 5, 1./3^(10^k)/10^k)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Benoit Cloitre, Aug 10 2003
STATUS
approved