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%I #21 Jun 27 2023 15:08:14
%S 0,5,8,6,6,1,0,2,8,7,3,4,3,3,7,2,9,6,5,8,4,2,2,5,5,4,8,0,8,1,5,1,1,3,
%T 2,6,2,4,1,8,5,8,6,1,0,7,8,2,2,6,5,9,8,3,4,3,6,1,2,1,1,0,2,3,9,8,9,2,
%U 9,9,6,5,4,6,3,9,8,4,6,3,6,9,1,6,5,1,2,3,5,9,4,5,3,9,9,3,3,9,7,8,0,7,8,9
%N Decimal expansion of largest Stoneham number S(3,2).
%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 2-normal.
%C Named after the mathematician Richard G. Stoneham (1920-1996). - _Amiram Eldar_, May 09 2022
%H David H. Bailey and Richard E. Crandall, <a href="https://doi.org/10.1080/10586458.2002.10504704">Random Generators and Normal Numbers</a>, Experimental Mathematics, Vol. 11, No. 4 (2002), pp. 527-546; <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-4/Random-Generators-and-Normal-Numbers/em/1057864662.full">alternative link</a>.
%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.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Stoneham_number">Stoneham number</a>.
%F S(3, 2) = Sum_{k>=1} 1/3^(2^k)/2^k.
%e 0.0586610287343372...
%t digits = 103; Clear[s]; s[n_] := s[n] = Sum[1/3^(2^k)/2^k, {k, 1, n}] // RealDigits[#, 10, digits]& // First // Prepend[#, 0]&; s[1]; s[n=2]; While[s[n] != s[n-1], n++]; s[n] (* _Jean-François Alcover_, Feb 15 2013 *)
%o (PARI) sum(k=1,6,1./3^(2^k)/2^k)
%Y Cf. A085137.
%K cons,nonn
%O 0,2
%A _Benoit Cloitre_, Aug 10 2003
%E Corrected from a(63) on by _Jean-François Alcover_, Feb 15 2013
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