A383820 Decimal expansion of Sum_{k>=1} 1/3^(3^k).

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

Offset: 0

Author

Artur Jasinski, May 16 2025

Keywords

• nonn
• cons

Comments

The real root of the cubic polynomial 243*x^3 - 27*x^2 - 242*x + 9 matches this constant to 20 decimal places.

Examples

			0.037087842300593465162409856...
		

Crossrefs

Cf. A008683, A383817, A383819.

Programs

Mathematica

sum = Sum[1/3^(3^n), {n, 1, Infinity}]; nsum = N[sum, 110]; RealDigits[nsum, 10, 105][[1]]

PARI

-sum(k=1,logint(2^getlocalbitprec(),3)+1,moebius(3*k)/(27.^k - 1),0.) \\ Bill Allombert

PARI

suminf(k=1, 1/3^(3^k)) \\ Amiram Eldar, May 16 2025

Formula

Equals -Sum_{k>=1} mu(3*k)/(27*k-1), where mu is the Möbius function A008683.

Equals A383817 - 1/3.