A072551 Decimal expansion of sqrt(e^(1/e)) = 1.20194336847031...

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

Offset: 1

Author

Benoit Cloitre, Aug 05 2002

Keywords

• cons
• nonn

Comments

This constant is related to the convergence properties of the following simple algorithm: w(n+2) = A^( w(n+1) + w(n) ) where A is a positive real. Take any w(1), w(2) reals>0, then w(n) converges if and only if, 0 < A < sqrt(e^(1/e)). For example if A=1/2 w(n) converges to 1/2, if A=1/3, w(n) converges to 0.408004405...(If w(n) converges the limit L is always independent of initial values w(1),w(2) and L is < e).

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.

Crossrefs

See also A073229 for e^(1/e).

Programs

Mathematica

RealDigits[E^(E^-1/2), 10, 110] [[1]]

Extensions

Edited by Robert G. Wilson v, Aug 08 2002