Grossman's Constant

Author

Eric W. Weisstein
January 27, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/GrossmansConstant.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GrossmansConstant.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Constant

c=0.73733830336929

Attempt to Solve the Recurrence

RSolve[{a[0]==1,a[1]==x,a[n+2]==a[n]/(1+a[n+1])},a[n],n]

RSolve[{a[0]==1,a[1]==.737338303369,a[n+2]==a[n]/(1+a[n+1])},a[n],n]

Plot of (Subscript[a, 1]), (Subscript[a, 2]), …

a[0]:=1
a[1]:=x
a[n_]:=a[n]=a[n-2]/(1+a[n-1])

a/@Range[7]//Factor

Plot[Evaluate[a/@Range[30]],{x,0,1},
PlotStyle->{Red,Blue},
AxesLabel->TraditionalForm/@{x,(Subscript[a, n])[x]},
Epilog->{Black,Line[{{c,0},{c,1}}]}]//Timing