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A347589
Continued fraction for Sum_{k>=0} 1/2^(3^k).
0
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
0,5
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
KEYWORD
nonn,cofr
AUTHOR
Benoit Cloitre, Sep 11 2021
STATUS
approved