This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347589 #32 Sep 30 2024 03:23:51
%S A347589 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,
%T A347589 2,511,1,1,1,1,1,7,2,1,1,1,2417851639229258349412351,2,1,2,7,1,1,1,1,
%U A347589 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
%N A347589 Continued fraction for Sum_{k>=0} 1/2^(3^k).
%F A347589 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.
%t A347589 ContinuedFraction[N[Sum[1/2^(3^k),{k,0,Infinity}],250]] (* _Stefano Spezia_, Sep 11 2021 *)
%o A347589 (PARI) my(v=contfrac(suminf(k=0, 1/2^(3^k)))); Vec(v, #v-1) \\ _Michel Marcus_, Sep 11 2021 and Sep 30 2024
%Y A347589 Cf. A007400.
%K A347589 nonn,cofr
%O A347589 0,5
%A A347589 _Benoit Cloitre_, Sep 11 2021