A225569 Decimal expansion of Sum_{n>=0} 1/10^(3^n), a transcendental number.

1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

According to the Thue-Siegel-Roth theorem, this number is transcendental.

As a sequence, characteristic sequence for powers of 3. - Franklin T. Adams-Watters, Aug 07 2013

Actually, characteristic function for 3^k - 1 (A024023), with the current starting offset 0. - Antti Karttunen, Nov 19 2017

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 171.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Wikipedia, Thue-Siegel-Roth theorem.

Index entries for characteristic functions.

Index entries for transcendental numbers.

Formula

From Antti Karttunen, Nov 19 2017: (Start)

a(n) = A063524(A053735(1+n)).

a(n) = abs(A154271(1+n)). (End)

From Amiram Eldar, Nov 02 2023: (Start)

With offset 1:

Completely multiplicative with a(3^e) = 1, and a(p^e) = 0 for p != 3.

Dirichlet g.f.: 1/(1-3^(-s)). (End)

Example

0.101000001000000000000000001000000000000000000000000000000000000000000000000000001...

Mathematica

(* n = 4 is sufficient to get 100 digits *) Sum[1/10^(3^n), {n, 0, 4}] // RealDigits[#, 10, 100]& // First

Prog

(PARI) a(n) = if(n+1 == 3^valuation(n+1, 3), 1, 0); \\ Amiram Eldar, Nov 02 2023

Crossrefs

Cf. A000244, A053735, A024023, A036987, A063524, A154271.

Sequence in context: A015829 A016334 A154271 * A087032 A236677 A190236

Adjacent sequences: A225566 A225567 A225568 * A225570 A225571 A225572

Keyword

nonn,easy,cons

Author

Jean-François Alcover, Jul 29 2013

Status

approved