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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
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.
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
KEYWORD
base,cons,nonn
AUTHOR
Benoit Cloitre, Aug 10 2003
STATUS
approved