A247844 Decimal expansion of the value of the continued fraction [1; 1, 2, 3, 4, 5, ...].

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

Offset

1,2

Comments

Equals 1+A052119.

Links

Table of n, a(n) for n=1..105.

MathOverflow, Is any particular algebraic number known to have unbounded continued fraction coefficients?

Eric Weisstein's MathWorld, Continued Fraction Constant

Eric Weisstein's MathWorld, Continued Fraction

Formula

1 + I_1(2) / I_0(2), where I_n(x) gives the modified Bessel function of the first kind.

Example

1.697774657964007982006790592551752599486658262998...

Mathematica

FromContinuedFraction[Join[{1}, Range[50]]] // RealDigits[#, 10, 105]& // First
(* or *) 1+BesselI[1, 2]/BesselI[0, 2] // RealDigits[#, 10, 105]& // First

Prog

(PARI) 1+besseli(1, 2)/besseli(0, 2) \\ Charles R Greathouse IV, Oct 23 2023

Crossrefs

Cf. A001040, A001053, A052119, A060997, A070910, A096789.

Sequence in context: A198135 A019813 A096767 * A052119 A021593 A378487

Adjacent sequences: A247841 A247842 A247843 * A247845 A247846 A247847

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 25 2014

Status

approved