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A225569 Decimal expansion of Sum_{n>=0} 1/10^(3^n), a transcendental number. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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)

EXAMPLE

0.101000001000000000000000001000000000000000000000000000000000000000000000000000001...

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A015829 A016334 A154271 * A087032 A236677 A190236

Adjacent sequences:  A225566 A225567 A225568 * A225570 A225571 A225572

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jul 29 2013

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)