A192014 Decimal expansion of Sum_{k>=1} 1/(3^k * 2^(3^k)).

0, 4, 1, 8, 8, 3, 6, 8, 0, 8, 3, 1, 5, 0, 2, 9, 8, 5, 0, 7, 1, 2, 5, 2, 8, 9, 8, 6, 2, 4, 5, 7, 1, 6, 8, 2, 4, 2, 6, 0, 9, 6, 7, 5, 8, 4, 6, 5, 4, 8, 5, 7, 5, 3, 5, 1, 8, 2, 8, 9, 2, 1, 9, 5, 4, 2, 0, 5, 0, 0, 6, 7, 2, 8, 9, 6, 6, 7, 1, 0, 6, 4, 5, 1, 8, 6, 5, 5, 7, 0, 7, 4, 2, 2, 6, 8, 1, 6, 8, 7, 0, 1, 4, 8, 1, 7, 3, 1, 9

Offset: 0

Author

Charles R Greathouse IV, Jun 22 2011

Keywords

• nonn
• cons
• easy

Comments

Stoneham proved that this number is 2-normal. David Bailey suggests a pseudorandom number generator based on it (though similar PRNGs could be based on other Stoneham numbers).

Examples

			0.0418836808315029850712528986245716824260967584654857535182892195420500672896...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• David H. Bailey and Richard E. Crandall, Random generators and normal numbers, Experimental Mathematics 11:4 (2004), pp. 527-546. [Alternate link]
• David H. Bailey, A pseudo-random number generator based on normal numbers (2004).
• R. Stoneham, On absolute (j,eps)-normality in the rational fractions with applications to normal numbers, Acta Arithmetica 22 (1973), pp. 277-286.
• Eric W. Weisstein, Stoneham Number.
• Index to sequences related to pseudo-random numbers

Programs

Mathematica

digits = 108; s = NSum[1/(3^n*2^3^n), {n, 1, Infinity}, WorkingPrecision -> digits + 5, NSumTerms -> 6]; Join[{0}, RealDigits[s, 10, digits] // First] (* Jean-François Alcover, Mar 07 2013, updated Mar 13 2015 *)

PARI

suminf(k=1,x=3^k;(1./x)>>x) \\ Charles R Greathouse IV, Jun 22 2011