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A085117 Decimal expansion of largest Stoneham number S(3,2). 2
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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

LINKS

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

FORMULA

S(3, 2)=sum(k>=1, 1/3^(2^k)/2^k) = 0.0586610287343372...

MATHEMATICA

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 *)

PROG

(PARI) sum(k=1, 6, 1./3^(2^k)/2^k)

CROSSREFS

Cf. A085137.

Sequence in context: A334849 A199265 A239382 * A301862 A245944 A160043

Adjacent sequences:  A085114 A085115 A085116 * A085118 A085119 A085120

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Aug 10 2003

EXTENSIONS

Corrected from a(63) on by Jean-François Alcover, Feb 15 2013

STATUS

approved

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Last modified January 22 19:45 EST 2022. Contains 350504 sequences. (Running on oeis4.)