A383817 -id:A383817 - cp's OEIS frontend

A055777 a(n) = 3^(3^n).

3, 27, 19683, 7625597484987, 443426488243037769948249630619149892803

Offset: 0

Henry Bottomley, Jul 12 2000

nonn

Next term is too big to include.
a(n+1) = a(n) written in base 3 and read as if in base 27 (and recorded in base 10).
Number of distinct n-ary operators in a ternary logic. - Ross Drewe, Feb 13 2008
The next term has 116 digits. - Harvey P. Dale, Mar 28 2019

Amiram Eldar, Table of n, a(n) for n = 0..6

Cf. A001146, A023365, A383817.

NestList[#^3&,3,5] (* Harvey P. Dale, Mar 28 2019 *)

print([3**(3**n) for n in range(5)]) # Michael S. Branicky, Mar 27 2021

a(n) = a(n-1)^3.

Sum_{n>=0} 1/a(n) = A383817. - Amiram Eldar, May 16 2025

A383819 Decimal expansion of -Sum_{k>=1} mu(3*k)/(27^k + 1), where mu is the Möbius function.

Original entry on oeis.org

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

Offset: 0

Artur Jasinski, May 16 2025

			0.034344352913278175288827529...

Cf. A008683, A383817, A383820.

Join[{0}, RealDigits[NSum[1/3^(3^k) - 2/3^(2*3^k), {k, 1, Infinity}, WorkingPrecision -> 120]][[1]]] (* Amiram Eldar, May 16 2025 *)

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

Equals Sum_{k>=1} (1/3^(3^k) - 2/3^(2*3^k)). - Amiram Eldar, May 16 2025

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

Original entry on oeis.org

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

Artur Jasinski, May 16 2025

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

			0.037087842300593465162409856...

Cf. A008683, A383817, A383819.

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

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

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

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

Equals A383817 - 1/3.

cp's OEIS Frontend

A055777 a(n) = 3^(3^n).

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A383819 Decimal expansion of -Sum_{k>=1} mu(3*k)/(27^k + 1), where mu is the Möbius function.

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

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