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

0,1

Comments

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

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

Example

0.681534914418223532301934163404812352676791108603519744242043855457416... - Harry J. Smith, Aug 24 2009

Mathematica

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

Prog

(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

Crossrefs

Equals A039661 - A059850.

Cf. A063503.

Sequence in context: A348435 A239804 A195716 * A188340 A350582 A011006

Adjacent sequences: A063501 A063502 A063503 * A063505 A063506 A063507

Keyword

easy,nonn,cons

Author

Robert G. Wilson v, Jul 30 2001

Extensions

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

Status

approved