OFFSET
0,1
COMMENTS
Since Mersenne numbers of the form 2^x - 1 consist entirely of 1's when written in binary, this continued fraction is nothing but 1's if written in binary.
Binary continued fraction: 1/(1+1/(11+1/(111+1/(1111+1/(11111+1/(111111+1/...
EXAMPLE
0.758542308171055739268126048842248893421247779...
MATHEMATICA
N[FromContinuedFraction[Table[2^k - 1, {k, 0, 100}]], 120] (* Vaclav Kotesovec, Nov 21 2019 *)
PROG
(PARI) dec_exp(v)= w=contfracpnqn(v); w[1, 1]/w[2, 1]+0.
dec_exp(vector(200, i, 2^(i-1)-1)) \\ Michel Marcus, Nov 21 2019
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Daniel Hoyt, Nov 21 2019
STATUS
approved