

A329810


Decimal expansion of the constant whose continued fraction representation is [0; 1, 3, 7, 15, 31, ...] = A000225 (the Mersenne numbers).


0



7, 5, 8, 5, 4, 2, 3, 0, 8, 1, 7, 1, 0, 5, 5, 7, 3, 9, 2, 6, 8, 1, 2, 6, 0, 4, 8, 8, 4, 2, 2, 4, 8, 8, 9, 3, 4, 2, 1, 2, 4, 7, 7, 7, 9, 7, 9, 6, 9, 5, 2, 8, 6, 0, 2, 9, 9, 5, 5, 2, 3, 9, 4, 0, 3, 1, 9, 0, 9, 5, 3, 5, 0, 9, 0, 9, 4, 0, 6, 7, 2, 3, 0, 8, 5, 9, 8
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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/...


LINKS

Table of n, a(n) for n=0..86.


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^(i1)1)) \\ Michel Marcus, Nov 21 2019


CROSSREFS

Cf. A000225, A052119, A073824.
Sequence in context: A280722 A262899 A198922 * A197726 A153623 A242623
Adjacent sequences: A329807 A329808 A329809 * A329811 A329812 A329813


KEYWORD

nonn,cons


AUTHOR

Daniel Hoyt, Nov 21 2019


STATUS

approved



