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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

Table of n, a(n) for n=0..103.

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-Fran├žois 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 August 10 08:22 EDT 2020. Contains 336368 sequences. (Running on oeis4.)