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

Offset: 0

Author

Benoit Cloitre, Sep 11 2021

Keywords

• nonn
• cofr

Crossrefs

Cf. A007400.

Programs

Mathematica

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

PARI

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

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.