%I #18 Jul 15 2018 13:49:40

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

%T 1,4,6,7,6,0,7,3,3,6,5,5,0,9,6,0,4,4,1,9,3,3,3,3,6,6,5,5,5,2,4,3,1,2,

%U 6,9

%N Decimal expansion of (BesselI(0,1/2)-BesselI(1,1/2))/(BesselI(0,1/2)-3*BesselI(1,1/2)).

%C The continued fraction of this number is the same as that of exp(1), except that a(3n) of the continued fraction of this number is the sequence of odd numbers, 2n+1, rather than the sequence of even numbers, 2n.

%e 2.77980607915035691390296218455... = 2 + 1/(1 + 1/(3 + 1/(1 + 1/(1 + 1/(5 + ...)))))

%t RealDigits[(BesselI[0, 1/2] - BesselI[1, 1/2])/(BesselI[0, 1/2] - 3 BesselI[1, 1/2]), 10, 70][[1]]

%o (PARI) (besseli(0, 1/2)-besseli(1, 1/2))/(besseli(0, 1/2)-3*besseli(1, 1/2)) \\ _Felix Fröhlich_, Jul 07 2018

%Y Cf. A001113, A003417, A058281, A101443, A298242.

%K nonn,cons

%O 1,1

%A _Terry D. Grant_, Jun 29 2018