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 A085137 Binary expansion of largest Stoneham number S(3,2). 2
 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
 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 Cf. A085117. Sequence in context: A000493 A011663 A091247 * A304577 A194670 A130543 Adjacent sequences:  A085134 A085135 A085136 * A085138 A085139 A085140 KEYWORD base,cons,nonn AUTHOR Benoit Cloitre, Aug 10 2003 STATUS approved

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Last modified September 20 05:58 EDT 2020. Contains 337264 sequences. (Running on oeis4.)