A347589 - OEIS

A347589

Continued fraction for Sum_{k>=0} 1/2^(3^k).

0, 1, 1, 1, 2, 7, 1, 1, 1, 1, 1, 511, 2, 1, 1, 1, 7, 2, 1, 1, 1, 134217727, 2, 1, 2, 7, 1, 1, 1, 2, 511, 1, 1, 1, 1, 1, 7, 2, 1, 1, 1, 2417851639229258349412351, 2, 1, 2, 7, 1, 1, 1, 1, 1, 511, 2, 1, 1, 1, 7, 2, 1, 2, 134217727, 1, 1, 1, 2, 7, 1, 1, 1, 2, 511, 1, 1, 1, 1, 1, 7, 2, 1, 1, 1

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..80.

FORMULA

a(5*2^k+2) = 2^(3^(k+1)) - 1. Other terms are obtained by symmetry around (5*2^k,5*2^k+1,5*2^k+2,5*2^k+3). For instance 1, 1, 1, 2, 7, 1, 1, 1, (1, 1, 511, 2), 1, 1, 1, 7, 2, 1, 1, 1.

MATHEMATICA

ContinuedFraction[N[Sum[1/2^(3^k), {k, 0, Infinity}], 250]] (* Stefano Spezia, Sep 11 2021 *)

PROG

(PARI) my(v=contfrac(suminf(k=0, 1/2^(3^k)))); Vec(v, #v-1) \\ Michel Marcus, Sep 11 2021 and Sep 30 2024

CROSSREFS

Cf. A007400.

Sequence in context: A364873 A377275 A011047 * A345930 A084794 A116691

Adjacent sequences: A347586 A347587 A347588 * A347590 A347591 A347592

KEYWORD

nonn,cofr

AUTHOR

Benoit Cloitre, Sep 11 2021

STATUS

approved