A085137 Binary expansion of largest Stoneham number S(3,2).

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

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-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