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A085138 Decimal expansion of largest "base 10" Stoneham number. 0
0, 0, 0, 0, 0, 1, 6, 9, 3, 5, 0, 8, 7, 8, 0, 8, 4, 3, 0, 2, 8, 6, 7, 1, 1, 0, 3, 6, 5, 9, 6, 7, 2, 4, 7, 5, 4, 0, 1, 7, 8, 4, 9, 5, 8, 2, 5, 5, 0, 2, 7, 9, 5, 5, 4, 7, 1, 5, 1, 8, 0, 8, 3, 6, 2, 3, 1, 6, 4, 9, 5, 8, 5, 4, 1, 6, 3, 4, 0, 4, 7, 2, 8, 2, 8, 2, 6, 1, 8, 0, 3, 5, 4, 6, 5, 8, 1, 6, 9, 7, 1, 8, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,7

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 normal in base 10.

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, 10)=0.00000169350878084302...

MATHEMATICA

digits = 99; Clear[s]; s[n_] := s[ n] = (rd = Sum[1/3^(10^k)/10^k, {k, 1, n}] // RealDigits[#, 10, 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) sum(k=1, 5, 1./3^(10^k)/10^k)

CROSSREFS

Cf. A085117, A085137.

Sequence in context: A072365 A239068 A259833 * A225053 A215483 A153872

Adjacent sequences:  A085135 A085136 A085137 * A085139 A085140 A085141

KEYWORD

cons,nonn

AUTHOR

Benoit Cloitre, Aug 10 2003

STATUS

approved

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Last modified August 10 08:35 EDT 2020. Contains 336368 sequences. (Running on oeis4.)