A247844 - OEIS

%I #11 Oct 23 2023 10:08:17

%S 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,

%T 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,

%U 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

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

%C Equals 1+A052119.

%H MathOverflow, <a href="http://mathoverflow.net/questions/177481">Is any particular algebraic number known to have unbounded continued fraction coefficients?</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ContinuedFractionConstant.html">Continued Fraction Constant</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/ContinuedFraction.html">Continued Fraction</a>

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

%e 1.697774657964007982006790592551752599486658262998...

%t FromContinuedFraction[Join[{1}, Range[50]]] // RealDigits[#, 10, 105]& // First

%t (* or *) 1+BesselI[1, 2]/BesselI[0, 2] // RealDigits[#, 10, 105]& // First

%o (PARI) 1+besseli(1,2)/besseli(0,2) \\ _Charles R Greathouse IV_, Oct 23 2023

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

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Sep 25 2014