A063504 Decimal expansion of e^Pi - Pi^e.

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

Offset: 0

Author

Robert G. Wilson v, Jul 30 2001

Keywords

• easy
• nonn
• cons

Comments

A classic calculus analysis problem is to discover whether e^Pi or Pi^e is the greater without the use of a calculator.

Examples

			0.681534914418223532301934163404812352676791108603519744242043855457416... - _Harry J. Smith_, Aug 24 2009
		

References

• Paul J. Nahin, When Least Is Best, How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible, Princeton University Press, Princeton NJ, 2004, Page 144.
• Alfred S. Posamentier & Ingmar Hehmann, Pi: A Biography of the World's Most Mysterious Number, Prometheus Books, NY 2002, pages 146, 301-304.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000

Crossrefs

Equals A039661 - A059850.

Cf. A063503.

Programs

Mathematica

RealDigits[N[E^Pi - Pi^E, 100]][[1]]

PARI

{ default(realprecision, 20080); e=exp(1); x=10*(e^Pi - Pi^e); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b063504.txt", n, " ", d)) } \\ Harry J. Smith, Aug 24 2009

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009