A329337 - OEIS

%I #6 Jun 13 2022 16:38:53

%S 0,1,1,1,1,40,1,3,2,1,2,23,1,13,1,8,1,15,2,3,103,4,10,4,2,2,2,1,1,84,

%T 1,4,1,3,1,1,5,1,7,23,8,1,8,24,1,1,2,12,39,14,19,3,4,8,3,2,1,4,1,8,1,

%U 1,1,2,1,10,1,35,1,10,2,2,2,1,1,15,2,3,1,4,7,5,1,9,1,1,1,1,2,3,3,2,1,4,54,4,1,3,2,1,1,1,1,4,22,1,4,3,1,1,1,2,6,1,1,4,1,8,1,20

%N Continued fraction of A328907 = 0.6009668516..., solution to 1 + 3^x = 6^x.

%e 0.6009668516... = 0 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + 1/(40 + 1/(1 + 1/(3 + ...)))))))

%t ContinuedFraction[x/.FindRoot[1+3^x==6^x,{x,1},WorkingPrecision->150]] (* _Harvey P. Dale_, Jun 13 2022 *)

%o (PARI) contfrac(c=solve(x=0,1, 1+3^x-6^x))[^-1] \\ discarding possibly incorrect last term. Use e.g. \p999 to get more terms. - _M. F. Hasler_, Oct 31 2019

%Y Cf. A328912 (cont. frac. of A242208: 1 + 2^x = 4^x), A328913 (cont. frac. of A328900: 2^x + 3^x = 4^x), A329335 (cont. frac. of A328905: 1 + 2^x = 5^x).

%K nonn,cofr

%O 0,6

%A _M. F. Hasler_, Nov 11 2019