%I #14 Jun 28 2023 08:20:08
%S 0,0,0,0,0,1,6,9,3,5,0,8,7,8,0,8,4,3,0,2,8,6,7,1,1,0,3,6,5,9,6,7,2,4,
%T 7,5,4,0,1,7,8,4,9,5,8,2,5,5,0,2,7,9,5,5,4,7,1,5,1,8,0,8,3,6,2,3,1,6,
%U 4,9,5,8,5,4,1,6,3,4,0,4,7,2,8,2,8,2,6,1,8,0,3,5,4,6,5,8,1,6,9,7,1,8,7,2
%N Decimal expansion of largest "base 10" Stoneham number.
%C 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.
%H D. H. Bailey and R. E. Crandall, <a href="http://www.emis.de/journals/EM/expmath/volumes/11/11.4/pp527_546.pdf">Random Generators and Normal Numbers</a>, Exper. Math. 11, 527-546, 2002.
%H R. Stoneham, <a href="https://eudml.org/doc/205168">On the Uniform Epsilon-Distribution of residues Within the Periods of Rational Fractions with Applications to Normal Numbers</a>, Acta Arithmetica, Vol. 22, No. 4 (1973), pp. 371-389.
%F S(3, 10) = 0.00000169350878084302...
%t 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 *)
%o (PARI) sum(k=1,5,1./3^(10^k)/10^k)
%Y Cf. A085117, A085137.
%K cons,nonn
%O 0,7
%A _Benoit Cloitre_, Aug 10 2003