A329810 Decimal expansion of the constant whose continued fraction representation is [0; 1, 3, 7, 15, 31, ...] = A000225 (the Mersenne numbers).

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

Offset: 0

Author

Daniel Hoyt, Nov 21 2019

Keywords

• nonn
• cons

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/...

Examples

			0.758542308171055739268126048842248893421247779...
		

Crossrefs

Cf. A000225, A052119, A073824.

Programs

Mathematica

N[FromContinuedFraction[Table[2^k - 1, {k, 0, 100}]], 120] (* Vaclav Kotesovec, Nov 21 2019 *)

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