A085117 Decimal expansion of largest Stoneham number S(3,2).

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

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.

Named after the mathematician Richard G. Stoneham (1920-1996). - Amiram Eldar, May 09 2022

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 (2002), pp. 527-546; alternative link.

R. Stoneham, On the Uniform Epsilon-Distribution of residues Within the Periods of Rational Fractions with Applications to Normal Numbers, Acta Arithmetica, Vol. 22, No. 4 (1973), pp. 371-389.

Wikipedia, Stoneham number.

Formula

S(3, 2) = Sum_{k>=1} 1/3^(2^k)/2^k.

Example

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